Business Statistics Assignment PDF

BUSINESS STATISTICS ASSIGNMENT Name: _____________________________________ Grade Awarded Father’s Name: _____________________________ Class: B. Com (Voc) FT – I Semester...

BUSINESS STATISTICS ASSIGNMENT Name: _____________________________________ Grade Awarded Father’s Name: _____________________________ Class: B. Com (Voc) FT – I Semester Ms. Akansha Edwards____________ Date:_____________ Instructions: you are required to take a printout of the assignment and tick the correct answers. For solution of numerical problems, you are required to attach separate plain A4 sheets at the back of the assignment and indicate chapter no. and question number on the solution. You are NOT REQUIRED to prepare separate copies for assignment. A printout of this assignment along with solution sheets attached at the back will be submitted. Date of Submission: 18th November, 2024 CHAPTER 1 MEASURES OF CENTRAL TENDENCY- MEAN, MEDIAN AND MODE 1. What is the mean of the data set {2, 4, 6, 8, 10 c) 4 }? d) 7 a) 4 6. The median of {1, 2, 3, 4, 5, 6, 7, 8, 9} is: b) 6 a) 4 c) 8 b) 5 d) 10 c) 5 2. If the median of the data set {3, 5, 7, 9, 11} is d) 6 7, what is the median of {5, 3, 11, 9, 7}? 7. If the mean of a set of values is greater than th a) 5 e median, the distribution is: b) 7 a) Symmetrical c) 9 b) Positively skewed d) 7 c) Negatively skewed 3. Which measure of central tendency is most ap d) Uniform propriate for categorical data? 8. Which measure is most affected by outliers in a) Mean the data set? b) Median a) Mean c) Mode b) Median d) Range c) Mode 4. In a perfectly symmetrical distribution, which d) Range measures are equal? 9. In a data set, if the mode is much less than the a) Mean and Mode mean, the distribution is likely: b) Median and Mode a) Symmetrical c) Mean and Median b) Uniform d) All of the above c) Negatively skewed 5. What is the mode of the data set {4, 4, 5, 6, 7, d) Positively skewed 4, 8, 9, 4, 5}? 10. What is the mean of the numbers 10, 20, 30, 4 a) 5 0, and 50? b) 6 a) 25  b) 30 19. In a set of data, which measure of central tend c) 35 ency is not affected by extreme values? d) 40 a) Mean 11. Which of the following represents a central ten b) Median dency measure? c) Mode a) Variance d) Standard deviation b) Standard Deviation 20. Which measure of central tendency can have c) Range more than one value? d) Median a) Mean 12. If the mean, median, and mode of a data set ar b) Median e all equal, the distribution is: c) Mode a) Positively skewed d) All of the above b) Negatively skewed 21. The average of a set of numbers is also known c) Symmetrical as the: d) Asymmetrical a) Mean 13. For a negatively skewed distribution, which re b) Mode lation is true? c) Median a) Mean > Median > Mode d) None of the above b) Mean < Median < Mode 22. The sum of the values in a data set divided by c) Mean < Median < Mode the number of values is the: d) Mean > Mode > Median a) Median 14. Which of the following best describes the mea b) Mean sure of central tendency that occurs most frequ c) Mode ently? d) Range a) Mean 23. If a data set has a median value that is higher t b) Mode han its mean, it is likely: c) Median a) Symmetrical d) None of the above b) Positively skewed 15. What is the median of {15, 18, 26, 28, 30}? c) Negatively skewed a) 15 d) Uniform b) 26 24. For a set of data points, the value that splits th c) 28 e set in half is the: d) 30 a) Mean 16. The mode of the data set {5, 5, 6, 7, 8, 5, 9, 7, b) Median 7} is: c) Mode a) 6 d) Range b) 7 25. The most frequently occurring value in a data c) 8 set is called the: d) 5 a) Mean 17. If a data set has two modes, it is called: b) Median a) Unimodal c) Mode b) Bimodal d) None of the above c) Multimodal 26. What is the mode of {2, 4, 4, 5, 6, 7, 7, 7, 8}? d) None of the above a) 4 18. What is the mean of the data set {2, 4, 6, 8, 10, b) 5 12}? c) 7 a) 5 d) 8 b) 6 27. If the mean of a data set is 24, what is the sum c) 7 of the data set if there are 12 values? d) 7 a) 48  b) 288 c) Mode c) 24 d) None of the above d) 12 36. If a data set has the same value repeated most f 28. The median of the data set {2, 3, 5, 7, 11, 13, 1 requently, it is called the: 7} is: a) Mean a) 7 b) Median b) 11 c) Mode c) 5 d) None of the above d) 3 37. What is the median of {2, 3, 5, 7, 8, 9, 12}? 29. What is the mean of the data set {4, 8, 12, 16} a) 5 ? b) 7 a) 12 c) 7 b) 10 d) 9 c) 10 38. In a data set with the values {4, 4, 5, 6, 6, 6, 7} d) 8 , the mode is: 30. The sum of the values divided by the count of a) 4 the values in a data set is the: b) 6 a) Median c) 5 b) Mean d) 7 c) Mode 39. For a positively skewed distribution, which rel d) Range ation holds true? 31. The measure of central tendency least affected a) Mean = Median = Mode by outliers is the: b) Mean < Median < Mode a) Mean c) Mean > Median > Mode b) Median d) Mean = Mode > Median c) Mode d) Range 40. Which measure of central tendency is often ref 32. If a distribution is negatively skewed, which m erred to as the 'average'? easure of central tendency is highest? a) Median a) Mode b) Mode b) Mean c) Mean c) Median d) None of the above d) Range 41. What is the mode of {6, 7, 7, 8, 9, 9, 9, 10}? 33. Which measure of central tendency represents a) 7 the middle value when all the values are order b) 8 ed? c) 10 a) Mean d) 9 b) Median 42. Which measure of central tendency divides the c) Mode data into two equal parts? d) Standard deviation a) Mean 34. What is the mode of the data set {1, 1, 2, 3, 3, b) Mode 3, 4, 4}? c) Median a) 1 d) None of the above b) 2 43. If the mean of the numbers 15, 20, and 25 is 2 c) 3 0, what is the total sum of these numbers? d) 4 a) 15 35. The average value in a set of data is known as b) 60 the: c) 20 a) Median d) 55 b) Mean 44. For a data set, which measure of central tende CHAPTER II ncy is the most robust to outliers? PARTITION VALUES – QUARTILES, a) Median DECILES AND PERCENTILES b) Mean c) Mode d) None of the above 45. What is the mean of the numbers 3, 5, 7, 9, an 1. What does the first quartile (Q1) represent in a d 11? data set? a) 7 a) 75th percentile b) 5 b) 25th percentile c) 7 c) 50th percentile d) 9 d) 90th percentile 46. Which of the following statements about the m 2. How many deciles divide a data set? ode is true? a) 4 a) The mode is always greater than the b) 5 mean. c) 12 b) The mode is always less than the me d) 10 dian. 3. In a normal distribution, what value does the 5 c) There can be more than one mode 0th percentile correspond to? in a data set. a) Q1 d) Both c and d are true. b) Q3 47. If the mean of a data set is 12 and the median i c) Median s 10, what can you infer about the distribution d) Mode ? 4. Which quartile corresponds to the 75th percent a) Positively skewed ile? b) Negatively skewed a) Q1 c) Symmetrical b) Q3 d) None of the above c) Median 48. The median of {5, 7, 9, 12, 15} is: d) Q2 a) 7 5. In terms of percentiles, the 90th percentile is al b) 9 so known as: c) 9 a) Q1 d) 12 b) P90 49. Which measure of central tendency is most ap c) Q2 propriate for ordinal data? d) D9 a) Median 6. What is the third quartile (Q3) value for the da b) Mean ta set {5, 7, 8, 12, 15, 18, 21}? c) Mode a) 12 d) Range b) 15 50. What is the mode of the data set {12, 15, 12, 1 c) 18 8, 20, 18, 20, 20}? d) 21 a) 15 7. Which of the following best describes a percen b) 18 tile rank? c) 20 a) A measure dividing data into 10 equ d) 12 al parts b) A measure dividing data into 100 eq ual parts c) A specific data point in a distributio n  d) A value below which a given percen a) 25th percentile tage of observations fall b) 50th percentile 8. If a student's test score is in the 95th percentile c) 75th percentile , it means they scored higher than: d) 90th percentile a) 5% of the students 17. In a box plot, which value is typically shown a b) 95% of the students s the central line inside the box? c) 90% of the students a) Q1 d) 75% of the students b) Q3 9. How many quartiles are in a data set? c) Median a) 2 d) Mode b) 4 18. Which measure would you use to identify outli c) 10 ers in a data set? d) 100 a) Mean 10. Which of the following is NOT a measure of p b) Standard deviation artition values? c) Interquartile range a) Quartiles d) Deciles b) Deciles 19. What is the 90th percentile value for the data s c) Percentiles et {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}? d) Standard deviation a) 12 11. The 40th percentile is also known as: b) 14 a) Q1 c) 18 b) Q3 d) 20 c) P40 20. The 60th percentile is located between which t d) D4 wo quartiles? 12. What is the second quartile (Q2) value for the a) Q1 and Q2 data set {10, 20, 30, 40, 50}? b) Q2 and Q3 a) 30 c) Q1 and Q3 b) 20 d) None of the above c) 40 21. If the 85th percentile is 250, it means: d) 50 a) 85% of the values are equal to 250 13. Which measure divides the data set into 100 e b) 85% of the values are more than 250 qual parts? c) 15% of the values are less than 250 a) Quartiles d) 85% of the values are less than 250 b) Deciles 22. The first decile (D1) is equivalent to which per c) Percentiles centile? d) None of the above a) 10th percentile 14. In a data set, if Q3 is 70 and Q1 is 30, what is t b) 20th percentile he interquartile range (IQR)? c) 30th percentile a) 100 d) 40th percentile b) 40 23. Which percentile corresponds to D5? c) 70 a) 25th percentile d) 30 b) 50th percentile 15. The 30th percentile is located between which t c) 75th percentile wo deciles? d) 90th percentile a) D3 and D4 24. If Q1 = 20, Q2 = 40, and Q3 = 60, the range of b) D2 and D3 the middle 50% of the data is: c) D1 and D2 a) 20 d) D4 and D5 b) 60 16. Which percentile is the same as the third quarti c) 40 le? d) 80 25. What does the term “decile” refer to in statistic c) Q2 s? d) None of the above a) A measure dividing data into 20 equ 33. Which of the following statements about quart al parts iles is true? b) A measure dividing data into 10 equ a) There are 5 quartiles in a data set al parts b) Q2 is the same as the median c) A measure dividing data into 4 equal c) Q3 is the lowest value in a data set parts d) Q1 is the highest value in a data set d) None of the above 34. If the median of a data set is 50, what is its per 26. The 20th percentile (P20) is the same as which centile rank? decile? a) 25th percentile a) D1 b) 75th percentile b) D2 c) 50th percentile c) D3 d) 50th percentile d) D4 35. In a data set, the first quartile (Q1) represents: 27. Which measure of partition values is best for c a) 25% of the values below Q1 omparing different data sets? b) 50% of the values below Q1 a) Quartiles c) 75% of the values below Q1 b) Percentiles d) 100% of the values below Q1 c) Deciles 36. What does the term “quartile” refer to in statist d) None of the above ics? 28. The 25th percentile is also known as: a) A measure dividing data into 10 equ a) Q1 al parts b) Q2 b) A measure dividing data into 100 eq c) Q3 ual parts d) D2 c) A measure dividing data into 4 equal 29. For a data set with a minimum value of 10 and parts a maximum value of 100, what is the range? d) None of the above a) 90 37. The 75th percentile is the same as: b) 90 a) Q1 c) 110 b) Q2 d) 80 c) Q3 30. Which of the following is NOT a characteristi d) D7 c of percentiles? a) They divide data into 100 equal part 38. If the third quartile (Q3) is 60, what is the inter s quartile range if Q1 is 30? b) They are useful for ranking a) 30 c) They represent central tendency b) 60 d) They help in understanding the distri c) 30 bution d) 45 31. If the 3rd quartile (Q3) value is 75 in a data set 39. The 9th decile (D9) is equivalent to which per , what is its percentile rank? centile? a) 25th percentile a) 25th percentile b) 50th percentile b) 50th percentile c) 75th percentile c) 75th percentile d) 100th percentile d) 90th percentile 32. The 5th decile (D5) is equivalent to which qua 40. Which measure divides data into 4 equal parts rtile? ? a) Q1 a) Deciles b) Q3 b) Quartiles  c) Percentiles c) Percentile d) None of the above d) Median 41. The 10th percentile (P10) is the same as: 50. The range of the middle 50% of a data set is k a) D2 nown as the: b) D1 a) Interquartile range c) Q1 b) Percentile d) D5 c) Quartile 42. In a data set, what is the value at the 50th perc d) Decile entile called? a) Q3 CHAPTER III b) Median MEASURES OF DISPERSION c) Q1 d) D5 43. Which of the following percentiles correspond 1. What is the range of the data set {4, 8, 6, 5, 9} s to the median of a data set? ? a) 25th percentile a) 5 b) 75th percentile b) 3 c) 50th percentile c) 5 d) 90th percentile d) 9 44. If a student's score is at the 70th percentile, ho 2. What does the variance measure in a data set? w many students scored higher than them? a) Central tendency a) 70% b) Skewness b) 50% c) Dispersion c) 30% d) Frequency d) 40% 3. If the standard deviation of a data set is 5, wha 45. The 25th percentile is also known as: t is the variance? a) Q2 a) 5 b) Q1 b) 25 c) Q3 c) 10 d) Median d) 50 46. Which measure of central tendency is not 4. Which measure of dispersion is most affected affected by extreme values? by extreme values? a) Median a) Range b) Mean b) Median c) Mode c) Mode d) None of the above d) Interquartile range 47. What does the 95th percentile indicate? 5. What is the coefficient of variation if the mean a) 5% of the data is above this value is 50 and the standard deviation is 10? b) 95% of the data is below this value a) 5% c) 95% of the data is above this value b) 20% d) 5% of the data is below this value c) 50% 48. What is the value of Q2 in a box plot? d) 10% a) Q1 6. What does a low standard deviation indicate a b) Median bout a data set? c) Q3 a) Data points are spread out d) P50 b) Data points are close to the mean 49. The measure that divides data into 100 equal p c) Data points are skewed arts is called: d) Data points are evenly distributed a) Quartile 7. What is the interquartile range (IQR) if Q3 is 7 b) Decile 5 and Q1 is 25?  a) 50 b) Average of data b) 50 c) Central point of data c) 100 d) None of the above d) 25 16. Which measure of dispersion is calculated as t 8. Which of the following is not a measure of dis he average of the squared differences from the persion? mean? a) Mean a) Range b) Mean b) Standard deviation c) Variance c) Variance d) Standard deviation d) Interquartile range 9. In a normal distribution, what percentage of da 17. If the standard deviation of a data set is 12, wh ta lies within one standard deviation of the me at is the variance? an? a) 12 a) 95% b) 24 b) 68% c) 144 c) 68% d) 36 d) 99% 18. What is the range of the data set {2, 3, 5, 7, 11 10. What is the range of the data set {15, 20, 30, 5 }? 0, 75}? a) 7 a) 60 b) 9 b) 75 c) 11 c) 45 d) 8 d) 30 19. Which measure of dispersion is least affected 11. The square of the standard deviation is called: by outliers? a) Mean a) Range b) Variance b) Interquartile range c) Range c) Standard deviation d) Median d) Variance 12. Which measure of dispersion is represented by 20. If the mean of a data set is 100 and the standar the symbol 'σ'? d deviation is 15, what is the coefficient of var a) Mean iation? b) Variance a) 15% c) Standard deviation b) 15% d) Range c) 85% 13. If the range of a data set is 45, what is the diffe d) 100% rence between the maximum and minimum val 21. In a data set with a mean of 50 and a standard ues? deviation of 5, what is the z- a) 22.5 score of the value 55? b) 45 a) 0.5 c) 50 b) 1 d) 30 c) 5 14. What is the coefficient of variation if the stand d) 10 ard deviation is 8 and the mean is 40? 22. What is the interquartile range of the data set { a) 4% 4, 8, 15, 16, 23, 42} if Q3 = 23 and Q1 = 8? b) 32% a) 30 c) 12% b) 15 d) 20% c) 8 15. What does the term "dispersion" refer to in stat d) 23 istics? 23. If the variance of a data set is 81, what is the st a) Spread of data andard deviation?  a) 8 b) Data points are close to the mean b) 9 c) Data points are skewed c) 10 d) Data points are evenly distributed d) 81 32. If the mean of a data set is 50 and the standard 24. Which of the following is a measure of relativ deviation is 5, what is the z- e dispersion? score of the value 45? a) Range a) -1 b) Variance b) -0.5 c) Interquartile range c) 0.5 d) Coefficient of variation d) 1 25. What is the range of the data set {10, 20, 30, 4 33. What is the variance of the data set {10, 12, 14 0, 50}? , 16, 18} if the standard deviation is 2.83? a) 30 a) 8 b) 40 b) 10 c) 20 c) 12 d) 50 d) 14 26. Which measure of dispersion is calculated by t 34. Which measure of dispersion is used to compa aking the square root of the variance? re the relative spread of two data sets? a) Standard deviation a) Range b) Mean b) Variance c) Range c) Interquartile range d) Median d) Coefficient of variation 27. In a normal distribution, what percentage of da 35. In a normal distribution, what percentage of da ta lies within two standard deviations of the m ta lies within three standard deviations of the ean? mean? a) 68% a) 68% b) 95% b) 95% c) 99% c) 99% d) 90% d) 90% 28. What is the standard deviation of the data set { 36. What is the interquartile range of the data set { 5, 5, 5, 5}? 1, 2, 3, 4, 5, 6, 7, 8, 9} if Q3 = 7 and Q1 = 3? a) 5 a) 4 b) 0 b) 4 c) 1 c) 6 d) 10 d) 8 29. If the range of a data set is 20 and the minimu 37. If the variance of a data set is 64, what is the st m value is 15, what is the maximum value? andard deviation? a) 30 a) 8 b) 35 b) 6 c) 35 c) 16 d) 25 d) 10 30. Which measure of dispersion is represented by 38. Which measure of dispersion is most appropri the symbol 'σ^2'? ate for ordinal data? a) Mean a) Standard deviation b) Variance b) Range c) Standard deviation c) Mean d) Range d) Variance 31. What does a high coefficient of variation indic 39. What is the range of the data set {10, 15, 20, 2 ate about a data set? 5, 30}? a) Data points are widely dispersed a) 10  b) 20 c) It is less sensitive to extreme values c) 15 d) None of the above d) 25 47. What does a standard deviation of zero indicat e? 40. Which measure of dispersion is calculated as t a) All data points are the same he difference between the maximum and mini b) Data points are evenly distributed mum values? c) Data points are widely spread out a) Standard deviation d) Data points are close to the mean b) Mean 48. Which measure of dispersion can be calculated c) Median for nominal data? d) Range a) Standard deviation b) Range 41. Which measure of dispersion can never be neg c) Variance ative? d) Interquartile range a) Variance 49. What is the range of the data set {9, 12, 15, 18, b) Range 21}? c) Interquartile range a) 9 d) Coefficient of variation b) 12 42. What does a high standard deviation imply ab c) 15 out the data set? d) 18 a) Data points are widely spread out 50. Which measure of dispersion is preferred whe b) Data points are close to the mean n the data set contains outliers? c) Data points are skewed a) Range d) Data points are equally distributed b) Interquartile range 43. What is the relationship between variance (σ²) c) Mean and standard deviation (σ)? d) Variance a) Variance is the square root of the sta 51. If the mean of a data set is 60 and the standard ndard deviation deviation is 12, what is the coefficient of variat b) Standard deviation is the square of t ion? he variance a) 10% c) Variance is the square of the standar b) 20% d deviation c) 20% d) There is no relationship d) 25% 44. In a data set, if Q1 is 25 and Q3 is 75, what is t 52. In a normal distribution, what percentage of da he semi-interquartile range? ta lies within three standard deviations of the a) 25 mean? b) 50 a) 99.7% c) 75 b) 95% d) 100 c) 68% 45. Which measure of dispersion is most sensitive d) 90% to extreme values? 53. What is the variance if the standard deviation i a) Median s 4? b) Range a) 16 c) Interquartile range b) 8 d) Mode c) 12 46. What is the main advantage of using the coeffi d) 4 cient of variation over standard deviation? 54. Which measure of dispersion is expressed in t a) It is easier to calculate he same units as the data? b) It allows comparison between data s a) Variance ets with different units b) Standard deviation  c) Range b) Standard deviation d) Coefficient of variation c) Interquartile range 55. If the range of a data set is 40 and the minimu d) Coefficient of variation m value is 20, what is the maximum value? 63. In a data set, what is the difference between th a) 50 e maximum and minimum values called? b) 60 a) Standard deviation c) 70 b) Range d) 80 c) Variance 56. What does the interquartile range measure? d) Interquartile range a) The spread of the middle 50% of dat 64. What is the interquartile range of the data set { a points 3, 6, 9, 12, 15, 18} if Q3 = 15 and Q1 = 6? b) The difference between the maximu a) 9 m and minimum values b) 6 c) The average distance of data points f c) 9 rom the mean d) 12 d) The variability of data points 65. Which measure of dispersion is least affected 57. Which measure of dispersion is most useful fo by extreme values? r skewed distributions? a) Range a) Standard deviation b) Interquartile range b) Range c) Standard deviation c) Interquartile range d) Coefficient of variation d) Mean 66. What is the variance if the standard deviation i 58. What is the coefficient of variation if the mean s 7? is 25 and the standard deviation is 5? a) 14 a) 10% b) 49 b) 20% c) 21 c) 30% d) 7 d) 40% 67. What is the coefficient of variation if the mean 59. What does a high coefficient of variation indic is 80 and the standard deviation is 16? ate about the data set? a) 20% a) Data points are close to the mean b) 40% b) Data points are widely dispersed c) 60% c) Data points are normally distributed d) 80% d) Data points are evenly distributed 68. In a normal distribution, what percentage of da 60. Which measure of dispersion is most appropri ta lies within one standard deviation of the me ate for interval and ratio data? an? a) Range a) 95% b) Standard deviation b) 68% c) Mode c) 99% d) Median d) 90% 61. What does the term "dispersion" refer to in stat 69. Which measure of dispersion is most useful fo istics? r comparing the spread of data sets with differ a) The spread of data points around a c ent units? entral value a) Range b) The central value of a data set b) Coefficient of variation c) The mode of a data set c) Standard deviation d) The sum of data points d) Variance 62. Which measure of dispersion is calculated as t 70. What is the main purpose of measuring dispers he square root of the variance? ion in a data set? a) Range a) To find the central value  b) To understand the variability of data 77. Which measure of central tendency is used mo points re frequently to calculate mean deviation in sk c) To determine the mode ewed distributions? d) To calculate the mean a) Mean b) Median 71. What is mean deviation also known as? c) Mode a) Standard deviation d) Range b) Variance 78. What is the mean deviation of the data set {1, c) Mean absolute deviation 2, 3, 4, 5} with respect to its mean? d) Interquartile range a) 1.2 72. What does mean deviation measure in a data s b) 0.8 et? c) 1.4 a) The average distance of data points f d) 1.0 rom the mean 79. If a data set has a mean deviation of 5 and a m b) The spread of the middle 50% of dat ean of 50, what is the coefficient of mean devi a points ation? c) The difference between the maximu a) 1% m and minimum values b) 10% d) The variability of data points around c) 5% the median d) 15% 73. How is mean deviation calculated for a data se 80. Why is mean deviation not as commonly used t? as standard deviation? a) By taking the square root of the vari a) It is harder to calculate ance b) It is less accurate b) By averaging the absolute difference c) It doesn't account for the direction of s from the mean deviations c) By summing up the squared differen d) It is sensitive to extreme values ces from the mean d) By calculating the range of the data set CHAPTER IV 74. What is the mean deviation of the data set {3, 6, 9} if the mean is 6? SKEWNESS a) 0 b) 1 c) 2 1. What does skewness measure in a data set? d) 3 a) Central tendency 75. Mean deviation can be calculated from which b) Asymmetry of the data distribution measures of central tendency? c) Dispersion a) Mean and median d) Frequency b) Only mean 2. If a distribution is positively skewed, the tail is c) Only median : d) Only mode a) Towards the left 76. Calculate the mean deviation of the data set {4 b) Symmetrical , 8, 12, 16, 20} with respect to its mean. c) Towards the right a) 6 d) Evenly distributed b) 4 3. What is the skewness of a perfectly symmetric c) 8 al distribution? d) 5 a) Positive b) Negative c) Zero  d) Undefined 12. What is the skewness of the data set {3, 6, 9, 1 4. In a negatively skewed distribution, the mean i 2, 15}? s: a) 1 a) Less than the median b) -1 b) Greater than the median c) 0 c) Equal to the mode d) 2 d) More than the mode 13. If the mean is less than the median, the distrib 5. What is the formula for calculating skewness i ution is: n a data set? a) Negatively skewed a) Mean / Standard deviation b) Positively skewed b) (Mean - Median) / Standard deviatio c) Symmetrical n d) Bimodal c) Variance / Mean 14. What does a skewness value of zero indicate? d) Median / Range a) Positively skewed 6. Which measure of central tendency is most aff b) Negatively skewed ected by skewness? c) Symmetrical distribution a) Mode d) None of the above b) Median 15. Which measure of skewness involves the third c) Mean central moment? d) Range a) Mode 7. For a positively skewed distribution, which of b) Median the following is true? c) Pearson’s coefficient a) Mean = Median = Mode d) Standard deviation b) Mean > Median > Mode 16. In a perfectly symmetrical distribution, the ske c) Mean < Median < Mode wness is: d) Mean = Mode > Median a) Positive 8. What is the skewness of a data set if the mean b) Negative is 20, the median is 15, and the standard deviat c) Undefined ion is 5? d) Zero a) 1 17. For a negatively skewed distribution, which re b) -1 lation is true? c) 0.5 a) Mean > Median > Mode d) 2 b) Mean < Median < Mode 9. If a distribution has a long left tail, it is: c) Mean = Median = Mode a) Negatively skewed d) Mean = Mode < Median b) Positively skewed 18. Which of the following distributions has a righ c) Symmetrical t-skewed tail? d) Bimodal a) Uniform distribution 10. Which skewness value indicates a highly skew b) Positively skewed distribution ed distribution? c) Normal distribution a) 0.5 d) Negatively skewed distribution b) 2 19. What is the skewness of a data set if the mean c) 0.1 is 25, the median is 30, and the standard deviat d) 1 ion is 5? 11. In a positively skewed distribution, the highest a) -0.5 value is the: b) 0.5 a) Mean c) -1 b) Mode d) 1 c) Median 20. What does a positive skewness indicate about t d) Range he distribution?  a) Tail is towards the left c) Equal to the mode b) Tail is towards the right d) Equal to the median c) Data is evenly distributed 29. What is the relationship between skewness and d) None of the above kurtosis? 21. In a data set, if the skewness is greater than 1, a) They both measure central tendency the distribution is: b) They both measure dispersion a) Symmetrical c) Skewness measures asymmetry, and b) Highly positively skewed kurtosis measures peakedness c) Highly negatively skewed d) They both measure frequency d) Moderately skewed 30. If the mean is greater than the mode, the distri 22. Which measure of skewness is based on the di bution is: fference between mean and mode? a) Negatively skewed a) Median skewness b) Positively skewed b) Pearson’s first coefficient c) Symmetrical c) Bowley’s coefficient d) Bimodal d) Standard deviation 31. What is the skewness of a data set if the mean 23. If the skewness of a distribution is - is 50, the median is 45, and the standard deviat 2, it indicates: ion is 5? a) Positively skewed a) 1 b) Negatively skewed b) -1 c) Symmetrical c) 0.5 d) Uniform d) 2 24. What is the skewness if the mean is 40, the me 32. Which measure of skewness is also known as t dian is 35, and the standard deviation is 10? he coefficient of skewness? a) 0.5 a) Mean skewness b) -0.5 b) Pearson’s coefficient c) 0.5 c) Bowley’s coefficient d) 1 d) Median skewness 25. In which skewness value range is a distributio 33. In a negatively skewed distribution, the mean i n considered approximately symmetrical? s: a) Between -2 and 2 a) Greater than the mode b) Between -0.5 and 0.5 b) Less than the median c) Between -1 and 1 c) Equal to the median d) Between -0.1 and 0.1 d) More than the mode 26. Which measure of skewness uses quartiles and 34. What does a positive skewness value indicate the median? about the mean and median? a) Bowley’s coefficient a) Mean is less than median b) Pearson’s first coefficient b) Mean is equal to median c) Median skewness c) Mean is greater than median d) Standard deviation d) Median is greater than mode 27. What does a negative skewness value indicate 35. In a symmetrical distribution, skewness is: about the tail of the distribution? a) Positive a) Tail is towards the right b) Negative b) Tail is towards the left c) Undefined c) Distribution is symmetrical d) Zero d) Distribution is bimodal 36. Which of the following distributions has a left- 28. In a positively skewed distribution, the mean i skewed tail? s: a) Uniform distribution a) Less than the median b) Positively skewed distribution b) Greater than the median c) Negatively skewed distribution  d) Normal distribution 45. Which measure of skewness can indicate the d 37. What is the skewness of the data set {2, 4, 6, 8 irection of skewness? , 10} if the mean is 6, the median is 6, and the a) Mean skewness standard deviation is 2? b) Median skewness a) 0.5 c) Pearson’s coefficient b) 0 d) Standard deviation c) -0.5 46. For a positively skewed distribution, the media d) 1 n is: 38. Which measure of skewness can be used for b a) Less than the mode oth small and large data sets? b) Less than the mean a) Mean skewness c) Equal to the mode b) Median skewness d) Greater than the mean c) Pearson’s coefficient 47. In a left-skewed distribution, the tail is: d) Standard deviation a) Towards the right 39. In a positively skewed distribution, the mode i b) Towards the left s: c) Symmetrical a) Less than the median d) Evenly distributed b) Greater than the median 48. What does a negative skewness value suggest c) Equal to the mean about the distribution? d) Equal to the range a) The distribution is symmetrical b) The tail is towards the right 40. What does a skewness value indicate about a d c) The tail is towards the left ata set? d) The distribution is bimodal a) Central tendency 49. In a positively skewed distribution, which of t b) Asymmetry of the data distribution he following is true? c) Dispersion a) Mean < Median < Mode d) Frequency b) Mean > Median > Mode 41. In a negatively skewed distribution, which val c) Mean = Median = Mode ue is the highest? d) Mode > Median > Mean a) Mean 50. What is the skewness of a data set if the mean b) Median is 30, the median is 25, and the standard deviat c) Mode ion is 10? d) Standard deviation a) -0.5 42. Which of the following skewness measures is b) 0.5 most affected by outliers? c) 0.75 a) Mean skewness d) -0.75 b) Median skewness 51. Which measure is least affected by skewness? c) Pearson’s coefficient a) Mean d) Bowley’s coefficient b) Median 43. What is the skewness if the mean is 100, the m c) Mode edian is 90, and the standard deviation is 15? d) Range a) 0.67 52. In a symmetrical distribution, the skewness is: b) -0.67 a) Positive c) 0.33 b) Negative d) -0.33 c) Zero 44. A distribution with a skewness value of -3 is: d) Undefined a) Symmetrical 53. What is the Pearson’s coefficient of skewness i b) Highly negatively skewed f the mean is 80, the mode is 70, and the stand c) Highly positively skewed ard deviation is 5? d) Moderately skewed a) 0.5  b) 2 d) Uniform c) 1.5 62. What is the main purpose of measuring skewn d) 0.8 ess in a data set? 54. A distribution with a skewness value of 3 is: a) To find the central value a) Highly positively skewed b) To understand the asymmetry of dat b) Highly negatively skewed a distribution c) Symmetrical c) To determine the mode d) Moderately skewed d) To calculate the mean 55. Which measure of skewness considers the diff 63. In a right-skewed distribution, the tail is: erences between quartiles? a) Towards the left a) Bowley’s coefficient b) Towards the right b) Pearson’s coefficient c) Symmetrical c) Mean skewness d) Evenly distributed d) Median skewness 64. What is the Pearson’s coefficient of skewness i 56. In a negatively skewed distribution, the media f the mean is 55, the median is 50, and the stan n is: dard deviation is 5? a) Greater than the mean a) 1 b) Greater than the mode b) 1 c) Less than the mean c) 0.5 d) Equal to the mode d) 2 57. What does a positive skewness value suggest a 65. Which measure of skewness is also known as t bout the mean and mode? he moment coefficient of skewness? a) Mean is less than mode a) Bowley’s coefficient b) Mean is equal to mode b) Pearson’s coefficient c) Mean is greater than mode c) Mean skewness d) Mode is greater than median d) Median skewness 58. Which of the following indicates a moderately 66. What is the skewness if the mean is 70, the mo skewed distribution? de is 60, and the standard deviation is 5? a) Skewness between -0.5 and 0.5 a) 2 b) Skewness less than -1 b) 1.5 c) Skewness between -1 and 1 c) 0.5 d) Skewness greater than 2 d) 3 59. What is the skewness if the mean is 45, the me 67. In a symmetrical distribution, the mean is: dian is 40, and the standard deviation is 5? a) Greater than the median a) 1 b) Less than the mode b) -1 c) Equal to the median c) 0.5 d) More than the median d) 1 68. Which of the following distributions has a righ 60. In a left- t-skewed tail? skewed distribution, which value is the lowest a) Uniform distribution ? b) Positively skewed distribution a) Median c) Normal distribution b) Mode d) Negatively skewed distribution c) Mean 69. What is the skewness of the data set {5, 10, 15 d) Range , 20, 25} if the mean is 15, the median is 15, a 61. If the skewness of a distribution is positive, th nd the standard deviation is 5? e distribution is: a) 0.5 a) Negatively skewed b) 0 b) Symmetrical c) -0.5 c) Positively skewed d) 1 70. What does a negative skewness value indicate 7. What does a positive correlation coefficient in about the mean and median? dicate? a) Mean is greater than median a) As one variable increases, the other b) Mean is equal to median variable also increases c) Mean is less than median b) As one variable increases, the other d) Median is greater than mode variable decreases c) No relationship between the variable s CHAPTER V d) Random relationship 8. What is the value of the correlation coefficient CORRELATION for a strong positive linear relationship? a) Close to 1 b) Close to 0 1. What does correlation measure? c) Close to -1 a) Central tendency d) Exactly 0 b) Strength and direction of the relation 9. If the correlation coefficient (r) is - ship between two variables 0.8, what can be inferred? c) Dispersion a) Strong positive correlation d) Frequency b) Weak positive correlation 2. What is the range of the correlation coefficient c) Strong negative correlation (r)? d) No correlation a) 0 to 1 10. What does a correlation coefficient of 0.5 indi b) -1 to 0 cate? c) -1 to 1 a) No correlation d) 0 to 2 b) Weak negative correlation 3. If the correlation coefficient (r) is 0, what does c) Strong negative correlation it imply? d) Moderate positive correlation a) Perfect positive correlation 11. Which of the following statements is true abou b) Perfect negative correlation t correlation? c) No correlation a) Correlation implies causation d) Strong correlation b) Correlation does not imply causatio 4. What does a correlation coefficient (r) of - n 1 indicate? c) Correlation always indicates a stron a) No correlation g relationship b) Weak correlation d) Correlation coefficient is always pos c) Perfect negative correlation itive d) Perfect positive correlation 12. In a scatter plot, what pattern indicates a positi 5. What is the correlation coefficient (r) if there i ve correlation? s a perfect positive relationship between two v a) Upward sloping pattern ariables? b) Downward sloping pattern a) 0 c) Horizontal pattern b) -1 d) Random pattern c) 0.5 13. What is the effect of outliers on the correlation d) 1 coefficient? 6. Which method is commonly used to calculate t a) Can significantly affect the value he correlation coefficient? b) Has no effect a) Mean c) Always increases the value b) Pearson’s method d) Always decreases the value c) Mode 14. Which of the following correlation coefficients d) Median indicates the weakest relationship?  a) -0.9 a) Outliers b) 0.7 b) Mean c) 0.1 c) Mode d) -0.5 d) Median 15. What is the purpose of a correlation matrix? 22. What type of correlation exists when an increa a) To find the mean of variables se in one variable results in a decrease in anoth b) To plot scatter diagrams er variable? c) To calculate the standard deviation a) Negative correlation d) To show the correlation coefficients b) Positive correlation between multiple variables c) No correlation 16. When should Spearman’s rank correlation be u d) Zero correlation sed instead of Pearson’s correlation? 23. Which correlation coefficient value represents a) When the data is normally distribute a perfect negative correlation? d a) 0 b) When the data is ordinal or not norm b) 1 ally distributed c) -1 c) When calculating standard deviation d) 0.5 d) When the data has outliers 24. If the correlation coefficient between variables 17. What is a partial correlation? X and Y is 0.85, what is the nature of their rel a) Correlation between two variables w ationship? hile controlling for a third variable a) Weak positive correlation b) Correlation between more than two b) Strong positive correlation variables c) No correlation c) Correlation between two categorical d) Strong negative correlation variables 25. What does a correlation of -0.3 indicate? d) Correlation without considering outl a) Strong positive correlation iers b) Weak positive correlation 18. Which type of correlation is used when both v c) Weak negative correlation ariables are ordinal? d) Strong negative correlation a) Pearson’s correlation 26. Which statistical tool is used to visualize the c b) Spearman’s rank correlation orrelation between two variables? c) Point-biserial correlation a) Box plot d) None of the above b) Histogram 19. What does a correlation coefficient close to - c) Scatter plot 1 signify? d) Pie chart a) Strong positive correlation 27. When the data points on a scatter plot form a p b) No correlation erfect straight line, the correlation coefficient i c) Strong negative correlation s: d) Moderate positive correlation a) 0 20. What is the key difference between correlation b) 0.5 and regression? c) 1 or -1 a) Correlation measures the relationshi d) 0.8 p, regression predicts the relationship 28. What is an example of a situation with no corr b) Correlation implies causation, regres elation? sion does not a) Height and weight c) Regression measures the relationshi b) Hours studied and grades p, correlation predicts the relationship c) Shoe size and intelligence d) There is no difference d) Income and expenditure 21. Which of the following can distort the true nat 29. Which type of correlation occurs when two va ure of the correlation coefficient? riables move in opposite directions?  a) Positive correlation b) Weak or no correlation b) Negative correlation c) Strong negative correlation c) Zero correlation d) None of the above d) Partial correlation 38. When is the point-biserial correlation used? 30. What is the correlation coefficient if X and Y a a) When both variables are continuous re independent? b) When both variables are ordinal a) 0 c) When one variable is continuous and b) 1 the other is dichotomous c) -1 d) When both variables are categorical d) 0.5 39. What does a correlation of -0.7 signify? 31. The value of the correlation coefficient (r) is th a) Strong positive correlation e same whether X is correlated with Y or: b) Weak positive correlation a) Y is correlated with Z c) Strong negative correlation b) Y is correlated with X d) No correlation c) Z is correlated with X d) X is correlated with Z 32. In a negative correlation, as one variable incre 40. What is the main purpose of calculating a corr ases, the other variable: elation coefficient? a) Decreases a) To find the mean of two variables b) Increases b) To plot scatter diagrams c) Remains the same c) To measure the strength and directio d) None of the above n of the relationship between two varia 33. Which correlation coefficient value suggests a bles weak positive relationship? d) To calculate the standard deviation a) 0.2 b) 0.9 c) -0.7 41. What does a positive correlation coefficient im d) -0.2 ply about the relationship between two variabl 34. What type of correlation exists between the nu es? mber of hours studied and exam scores? a) One variable decreases as the other i a) Negative correlation ncreases b) Positive correlation b) Both variables increase together c) No correlation c) One variable remains constant as the d) Zero correlation other changes 35. What does a correlation coefficient of 1 imply d) No relationship ? 42. Which correlation coefficient value suggests th a) No correlation e strongest relationship? b) Weak positive correlation a) 0.2 c) Perfect positive correlation b) 0.9 d) Strong negative correlation c) -0.5 36. Which of the following can be used to interpre d) 0.3 t the strength of a correlation? 43. What is the primary purpose of using correlati a) Mean on analysis? b) Median a) To find the mean of data c) Correlation coefficient (r) b) To measure the strength and directio d) Mode n of the relationship between two varia 37. If the correlation coefficient is close to zero, w bles hat can be inferred about the relationship betw c) To identify the mode een the variables? d) To calculate the median a) Strong positive correlation 44. What does a scatter plot show?  a) The relationship between two variab d) Constant correlation les 52. What is the purpose of a scatter plot in correlat b) The frequency distribution of a varia ion analysis? ble a) To calculate the mean c) The mean and median of a variable b) To visualize the relationship betwee d) The range and standard deviation of n two variables a variable c) To find the range 45. What is the result when the correlation coeffici d) To determine the mode ent is squared? 53. Which measure is used to determine the streng a) Coefficient of determination (R²) th of a linear relationship between two variabl b) Mean es? c) Standard deviation a) Mean d) Mode b) Median 46. If two variables have a correlation coefficient c) Correlation coefficient of 0.95, how would you describe their relation d) Mode ship? 54. In which scenario would you expect to find a n a) Weak positive correlation egative correlation? b) Strong positive correlation a) As temperature increases, ice cream c) No correlation sales increase d) Moderate negative correlation b) As the number of hours worked incr 47. Which correlation method is used for non- eases, leisure time decreases parametric data? c) As income increases, spending incre a) Pearson’s correlation ases b) Spearman’s rank correlation d) As age increases, experience increas c) Regression es d) Mode 55. If the correlation coefficient between X and Y 48. What is the implication of a correlation coeffic is -0.4, what type of relationship do they have? ient close to zero? a) Positive correlation a) Strong positive relationship b) Negative correlation b) Weak or no relationship c) No correlation c) Perfect positive relationship d) Perfect correlation d) Strong negative relationship 56. What does a correlation coefficient of - 49. If the correlation coefficient is 0.6, what is the 0.95 indicate? percentage of the variation in one variable that a) Weak positive correlation is explained by the other variable? b) Strong negative correlation a) 36% c) No correlation b) 36% d) Strong positive correlation c) 60% 57. What is the relationship between correlation a d) 16% nd causation? 50. What does the symbol 'r' represent in statistics a) Correlation always implies causation ? b) Correlation sometimes implies causa a) Mode tion b) Standard deviation c) Correlation does not imply causation c) Correlation coefficient d) There is no relationship d) Mean 58. When is Pearson’s correlation most appropriat 51. What type of correlation is indicated by a dow e to use? nward sloping pattern in a scatter plot? a) For ordinal data a) Negative correlation b) For continuous data with a linear rel b) Positive correlation ationship c) No correlation c) For categorical data  d) For non-linear relationships d) Can significantly distort the correlati 59. If the correlation coefficient (r) between height on and weight is 0.75, what does this imply? 66. What does a correlation coefficient close to - a) There is a strong positive relationshi 1 indicate? p between height and weight a) A strong negative relationship b) There is no relationship between hei b) A weak positive relationship ght and weight c) No relationship c) There is a strong negative relationshi d) A moderate positive relationship p between height and weight 67. If the correlation coefficient between two varia d) Height and weight are independent bles is 0.85, what percentage of the variation is 60. What does a scatter plot with a perfect upward explained by this relationship? slope indicate about the correlation coefficient a) 72.25% ? b) 85% a) It is 1 c) 68% b) It is 0 d) 95% c) It is -1 68. What is an example of a negative correlation i d) It is undefined n real life? 61. Which term describes a situation where two va a) As the temperature increases, the de riables move in the same direction? mand for heating decreases a) Negative correlation b) As income increases, spending incre b) Positive correlation ases c) Zero correlation c) As education level increases, income d) Partial correlation increases 62. If a correlation coefficient is negative, what do d) As the number of study hours increa es it mean? ses, exam scores increase a) There is no relationship 69. Which correlation method is used when one va b) As one variable increases, the other riable is binary and the other is continuous? decreases a) Pearson’s correlation c) As one variable decreases, the other b) Point-biserial correlation decreases c) Spearman’s rank correlation d) Both variables remain constant d) None of the above 63. What is the correlation coefficient if the relatio 70. What does a correlation coefficient of 0.2 indi nship between two variables is weak but positi cate? ve? a) Strong positive correlation a) -0.9 b) Strong negative correlation b) 0.3 c) No correlation c) 0.9 d) Weak positive correlation d) -0.3 71. If the correlation coefficient is 0.9, what does t 64. Which correlation method is suitable for non- he scatter plot look like? linear relationships? a) Points are closely clustered around a a) Spearman’s rank correlation n upward sloping line b) Pearson’s correlation b) Points are scattered with no pattern c) Point-biserial correlation c) Points are closely clustered around a d) Linear regression downward sloping line 65. In correlation analysis, what does an outlier do d) Points form a horizontal line ? 72. What is the implication of a zero- a) Has no effect on the correlation correlation coefficient? b) Always increases the correlation a) Strong positive relationship c) Always decreases the correlation b) Strong negative relationship c) No linear relationship  d) Moderate positive relationship 80. How does the sign of a correlation coefficient 73. In a positive correlation, as one variable increa (+/-) impact its interpretation? ses, what happens to the other variable? a) It indicates the direction of the relati a) It also increases onship b) It decreases b) It indicates the strength of the relatio c) It remains constant nship d) It fluctuates randomly c) It indicates no relationship 74. Which value of the correlation coefficient indi d) It indicates the mean value of the va cates the strongest relationship? riables a) 0.5 b) 1 c) -0.5 81. What does the coefficient of correlation (r) me d) 0 asure in relation to regression coefficients? 75. What does a correlation coefficient of - a) The intercept of the regression line 0.2 signify? b) The strength and direction of the lin a) Strong positive correlation ear relationship between two variables b) Strong negative correlation c) The slope of the regression line c) Weak negative correlation d) The standard error of the estimate d) No correlation 82. If the coefficient of correlation (r) is positive, 76. How are the regression coefficients related to c what can be said about the slope of the regress orrelation coefficient in a linear regression mo ion line? del? a) The slope is zero a) They measure the strength of the lin b) The slope is positive ear relationship between the dependent c) The slope is negative and independent variables d) The slope is undefined b) They determine the mean 83. What does a negative coefficient of correlation c) They identify the mode (r) indicate about the relationship between the d) They calculate the standard deviatio regression coefficients? n a) Both coefficients are positive 77. When the correlation coefficient is 0.1, what d b) One coefficient is positive, and the o oes this suggest about the relationship? ther is zero a) Very weak positive relationship c) One coefficient is positive, and the o b) Strong positive relationship ther is negative c) Weak negative relationship d) Both coefficients are negative d) Strong negative relationship 84. How is the coefficient of correlation (r) related 78. What is the coefficient of determination if the to the coefficients of regression (b1 and b2)? correlation coefficient is 0.7? a) r = sqrt(b1 * b2) a) 49% b) r = b1 + b2 b) 0.7% c) r = b1 - b2 c) 49% d) r = b1 / b2 d) 70% 85. In a simple linear regression model, what does the coefficient of correlation (r) indicate if it i 79. What does the value of a correlation coefficien s close to 1? t depend on? a) A strong positive linear relationship a) Only the mean of the variables between the dependent and independen b) The covariation between the variabl t variables es b) A weak negative relationship betwe c) Only the mode of the variables en the dependent and independent vari d) The standard deviation of the variabl ables es  c) No relationship between the depend d) r is the product of the regression coe ent and independent variables fficients d) A non- linear relationship between the depend ent and independent variables ---------x------x------x-------x-x-------x-------x------x---- 86. What does it mean if the regression coefficient is zero and the coefficient of correlation is als o zero? a) There is a perfect positive relationsh ip between the variables b) There is a perfect negative relations hip between the variables c) There is no linear relationship betwe en the variables d) The regression line passes through t he origin 87. How is the coefficient of determination (R²) re lated to the coefficient of correlation (r)? a) R² = r² b) R² = r c) R² = sqrt(r) d) R² = 1 - r 88. In the context of regression analysis, what doe s the coefficient of correlation (r) represent? a) The average of the independent vari able b) The maximum value of the depende nt variable c) The degree of linear association bet ween the dependent and independent v ariables d) The difference between the highest a nd lowest values 89. If the slope of the regression line is negative, what can be inferred about the coefficient of c orrelation (r)? a) r is positive b) r is zero c) r is negative d) r is undefined 90. What is the relationship between the coefficien t of correlation (r) and the regression coefficie nts in a bivariate regression model? a) r is the difference between the regres sion coefficients b) r is the sum of the regression coeffic ients c) r is the geometric mean of the regres sion coefficients