11 Statistics Past Papers Lahore 2012-2018 PDF

# Chapter Wise Past Papers ## 11 Statistics **Class:** Intermediate Part I (11th) **Board:** Lahore **Period:** 2012 - 2018 **Prepared by:** Muhammad Nadeem Assistant Professor Govt. Khawaja Rafique Shaheed College, Walton Road, Lahore ## Contents * Pattern of Question Paper 2018 * Chapter...

# Chapter Wise Past Papers ## 11 Statistics **Class:** Intermediate Part I (11th) **Board:** Lahore **Period:** 2012 - 2018 **Prepared by:** Muhammad Nadeem Assistant Professor Govt. Khawaja Rafique Shaheed College, Walton Road, Lahore ## Contents * Pattern of Question Paper 2018 * Chapter 01: Introduction * Chapter 02: Presentation of Data * Chapter 03: Measures of Central Tendency * Chapter 04: Measures of Dispersion * Chapter 05: Index Numbers * Chapter 06: Set Theory * Chapter 07: Probability * Chapter 08: Random Variables and Probability Distributions * Chapter 09: Binomial and Hypergeometric Distributions ## Pattern of Question Paper 2018 | Chapter | MCQ | Short Questions | Long Questions | | -------- | ---- | --------------- | --------------- | | 01 Introduction | 1 | 2 | 0 | | 02 Presentation of Data | 2 | 2 | 2 | | 03 Measures of Central Tendency | 3 | 5 | 2 | | 04 Measures of Dispersion | 3 | 2 | 2 | | 05 Index Numbers | 2 | 5 | 1 | | 06 Set Theory | 2 | 5 | 1 | | 07 Probability | 2 | 5 | 1 | | 08 Random Variables and Probability Distributions | 0 | 4 | 2 | | 09 Binomial and Hypergeometric Distributions | 2 | 4 | 2 | ### Pairing of Short Questions * **Group 1:** 1, 3, 5 * **Group 2:** 2, 4, 6 * **Group 3:** 7, 8, 9 ### Pairing of Long Questions * **Question 1:** 3, 3 * **Question 2:** 4, 4 * **Question 3:** 5, 6 * **Question 4:** 8, 8 * **Question 5:** 9, 9 ## Chapter 01: Introduction ### Multiple Choice Questions 1. Colour of hair is a: * A) Continuous Variable * **B) Discrete Variable** * C) Qualitative Variable * D) Quantitative Variable 2. A quantity calculated from a population is called: * A) Frequency * **B) Statistic** * C) Parameter * D) Sample 3. The branch of Statistics which deals with procedures of drawing inference about the population on the basis of sample information is called * A) Descriptive Statistics * **B) Inferential Statistics** * C) Applied Statistics * D) Theoretical Statistics 4. Smoking habits of residents of a city are: * **A) Qualitative Data** * B) Quantitative Data * C) Discrete Data * D) Continuous Data 5. A quantity calculated from the sample is called: * **A) Statistic** * B) Sample * C) Parameter * D) None of these 6. The grouped data is: * **A) Primary Data** * B) Secondary Data * C) Raw Data * D) None of these 7. Statistic is a characteristic calculated from: * **A) Population Data** * B) Sample Data * C) Arrayed Data * D) Fictitious Data 8. Brand of a soap is _______ variable: * A) Quantitative * **B) Qualitative** * C) Imaginary * D) Continuous ### Short Questions 1. Differentiate between continuous and discrete variables. 2. What is primary data? 3. Define population and sample. 4. Write sources of secondary data. 5. Define Statistics. 6. Define population and sample. 7. Define descriptive statistics. 8. Define statistics as a discipline of science. 9. Define population. 10. Define secondary data. 11. Write down the characteristics of statistics. 12. Define statistics and data. 13. Distinguish between primary and secondary data. ### Long Questions * No questions ## Chapter 02: Presentation of Data ### Multiple Choice Questions 1. An ogive is a: * A) Frequency Polygon * C) Cumulative Frequency * **B) Frequency Curve** * D) None of these 2. The difference between largest and smallest value is: * A) Interval * C) Range * **B) SD** * D) None of these 3. What is total angle of pie diagram? * A) 90° * C) 360° * B) 180° * **D) None of these** 4. The average of lower and upper limits of a class is called: * **A) Class Mark** * B) Class Frequency * C) Class Boundary * D) Relative Frequency 5. Cumulative frequency curve is also called: * A) Histogram * **C) Ogive** * B) Histogram * D) Frequency Curve 6. Pie diagram consists of: * **A) Circle** * B) Bars * C) Rectangles * D) All of these 7. The frequency of a class divided by total frequency is called: * A) Class Frequency * **C) Relative Frequency** * B) Cumulative Frequency * D) Total Frequency 8. How many methods are used for the collection of data? * A) 1 * **B) 2** * C) 3 * D) 4 9. In a percentage frequency distribution, the total of percentage frequencies is: * A) 1 * C) Ef * **B) 100** * D) Ex 10. The graphic representation of the frequency distribution is: * A) Frequency Curve * C) Ogive * **B) Histogram** * D) Histogram 11. A graph of cumulative frequency curve is called: * A) Histogram * C) Bar Chart * **B) Pie Chart** * D) Ogive 12. Headings for different columns in a table are called: * A) Stub * C) Column captions * **B) Title** * D) Prefatory note ### Short Questions 1. Differentiate between classification and tabulation. 2. How a frequency polygon is constructed? 3. Differentiate between histogram and histogram. 4. Enlist the main parts of a table. 5. Explain the simple classification. 6. Define class marks. 7. What is meant by frequency distribution? 8. Distinguish between one-way classification and two ways classification. 9. What do you mean by term classification? 10. Define histogram. 11. What is class boundary. 12. Differentiate between class limits and class boundaries. 13. What is meant by relative frequency of a class? ### Long Questions * No questions ## Chapter 03: Measures of Central Tendency ### Multiple Choice Questions 1. If the Mean = 40, Mode = 42, the distribution is: * A) Symmetrical * **C) Negatively skewed** * B) Positively skewed * D) None of these 2. The sum of deviation from mean is: * A) 5 * C) ) 3 * **B) Zero** * D) 1 3. The modal letter of the word "STATISTICS" is: * A) No mode * C) T * **D) S and T** 4. Which of the following averages is affected by extreme values? * **A) Arithmetic Mean** * B) Median * C) Mode * D) All of these 5. The observation which occurs maximum number of times is called: * A) Mean * C) Mode * B) Median * D) H.M. 6. Arithmetic mean for X1 and X2: * **A) * B) 2X1X2 * C) X1+X2 * D) X1X2 7. If Σ(x - 20) = 25, Σ(Χ - 15) = 0 and 2(x - 10) = -10 then arithmetic mean is: * A) 25 * **C) 15** * B) -10 * D) 20 8. Suitable average for averaging to shoe sizes is: * A) Mean * B) Median * C) Mode * **D) Geometric Mean** 9. Mean is affected by change of: * A) Origin * B) Scale * C) Both A and B * **D) None of these** 10. Geometric mean of 2, 4, 8 is: * A) Zero * B) 16 * **C) 8** * D) 4 11. A symmetrical distribution has mean = 4 then its mod is * A) 4 * B) less than 4 * **C) Greater than 4** * D) Zero 12. If a and b are two values, then geometric mean is: * A) a x b * C) a+b * **B) √a x b** * D) a+b 13. In a symmetrical distribution: * **A) Mean = median = mode** * B) Mean > median > mode * C) Mean < median < mode * D) Mean > median < mode 14. Σ(y - y) = * A) 0 * C) Least * **B) 1** * D) Minimum 15. In qualitative data, the most suitable average is: * A) Arithmetic mean * C) Harmonic mean * **B) Geometric Mean** * D) Mode ### Short Questions 1. What is weighted arithmetic mean? 2. State some disadvantages of the mode. 3. The sum of deviation of 10 values from 15 is 20. Find Arithmetic Mean. 4. If Mean = 20, Median = 18.67, find Mode? 5. Find G.M. if X= 1,3,9 6. Define quartiles. 7. Describe empirical relation between mean, median and mode. 8. For a certain distribution, if Σ (Χ – 15) = 5, Σ (Χ – 18) = 0 and Σ (Χ – 21 ) = - - 21, then what is the value of mean and why? 9. Write any two properties of arithmetic mean. If mean = 20, median = 18, find mode for a set of data? 10. What is central tendency? 11. Define Median. 12. Give two properties of Arithmetic Mean. 13. Find the mode of 3, 3, 7, 8, 10, 11, 10, 12 14. Define geometric mean. 15. Write any two qualities of a good average. 16. Define mode with formula. 17. The sum of deviations of 15 values from 20 is 45. Find arithmetic mean. 18. If mode = 15 and mean = 10.5. Find median. 19. Write the types of average. 20. Write two properties of A M. * 21. Define geometric mean with formula 22. Given 1 = 200.fm = 25, f₁ = 20, f2 = 20, h = 10, find mode. 23. (X-170) Given Σfu = 100, Σf = 200. Find X 5 24 What is meant by measure of central tendency? 25. Define geometric mean. 26. x-170 Given u ∑ fu = 200, find arithmetic mean. 5 27. In a moderately skewed distribution, the values of mean and median are 120 and 110 respectively. Find the value of mod. 28. Define the term median. 29. Write down any two mathematical properties of arithmetic mean. 30. Define mode and give its formula in case of grouped data. 31. The mean of ten values is 20. If one more value is included, the mean becomes 22, find included value? 32. If geometric mean of 3 items is 7, find the product of all items? ### Long Questions * A variable Y i determined from a variable X by using the equation Y = 10 − 4X. Find Y when X = 3, 2, 1, 0, 1, 2, 3, 4, 5 and show that Y = 10-4X * Compute mode of the data given below: Hourly wages 4-6 6-8 8-10 10-12 12-14 14-16 f 13 111 182 105 19 7 * Salman obtained the following marks in a certain examination. Find weighted mean if weights 4, 3, 3, 2 respectively are allotted to subjects. English Urdu Maths Stats Physics 73 82 80 57 62 * Compute weighted arithmetic mean: Subject Marks Eng. Urdu Math. Eco. 73 85 92 65 Weight 3 3 4 3 * Calculate median for the given data: Groups 15-19 20-24 25-29 30-34 35-39 f 4 8 12 9 3 * Find the Arithmetic Mean from the following data: X-30 u = 5 f -2 -1 0 1 2 3 5 8 15 20 12 4 * Find the H.M. from the data given below: X 10 12 14 16 18 20 f 1 3 7 12 8 1 * Calculate Harmonic Mean of the data given below. Also calculate Mode and P40 of this data. Weight 40-44 45-49 50-54 55-59 f 20 30 40 10 * Reciprocals of x are given below. Calculate harmonic mean of the data and also arithmetic mean. 0.0267, 0.02350.0211, 0.0191, 0.0174, 0.0160, 0.0148 * A man gets a rise of 10% in salary at the end of his first year of service and further rises of 20% and 25% at end of the second and third year respectively. The rise in each case being calculated on his salary at the beginning of the year. What is annual percentage average increase? * Find average of 10 km/h, 20 km/h and 25 km/h. * Compute mode and median of the data given below: Wages 4-6 6-8 8-10 10-12 12-14 14-16 Employees 13 110 180 105 18 8 ## Chapter 04: Measures of Dispersion ### Multiple Choice Questions 1. If X and Y are two independent variables, then E (XY) = * A) E(X) + E(Y) * C) E (X) - E (Y) * **B) E(X).E(Y)** * D) Zero 2. Standard deviation of 3, 3, 3, 3, 3 is equal to: * A) 8 * C) Zero * B) ) 3 * **D) ) 16** 3. First moment about mean is equal to: * A) One * C) Zero * **D) All of these** 4. In a negatively skewed distribution: * **A) Mean = Mode** * C) Mode > Mean * B) Mean > Mode * D) None of these 5. If var (X) = 9, then var(2X + 4) is: * A) 36 * C) 18 * **B) 10** * D) 6 6. The range of the scores 19, 3,140, 25, 95 is: * **A) 140** * B) 3 * C) 137 * D) 143 7. Coefficient of Quality Deviation is: * Q3-Q1 A) Q3+Q1 * Q3 - Q1 B) Q3+Q1 * Q1+3 C) Q1-3 * Q1-3 D) Q1+3 8. The value of standard deviation changes by a change of: * A) Origin * **B) Scale** * C) Algebraic sign * D) Both A and B 9. The variance of 5, 5, 5, 5 and 5 is: * A) Zero * C) 5 * **B) 25** * D) 125 10. In a symmetrical distribution Q1 = 4, Q3 = 12, then median is: * A) 4 * C) 8 * **B) 6** * D) Zero 11. If Q3 = 20, Q1 = 10 the coefficient of quartile deviation is: * A) 3 * C) 2 * **B) 1 / 3** * D) 1 12. Sum of absolute deviations of the values is least, when deviations are taken from: * A) Mean * C) Mode * **B) Median** * D) G.M. 13. In a symmetrical distribution the coefficient of skewness will always be: * A) Negative * C) 1 * **B) Zero** * D) -1 14. Second moment about mean is: * A) Variance * C) Zero * **B) Standard Deviation** * D) One 15. If ẞ2 = 3, then the distribution is called: * A) Symmetrical * **B) Mesokurtic** * C) Platykurtic * D) Leptokurtic 16. If y₁ = ax + b then var(y₁) is : * A) a var(x₁) + b * C) a var (x₁) * **B) var(x₁) ** * D) a²var(x₁) 17. If moment ratio b1 = 0 then distribution is: * A) Symmetrical * C) U-shaped * **B) J-shaped** * D) all of these 18. Variance of 3, 3, 3, 3 is: * A) 3 * C) Positive * **B) Negative** * D) Zero 19. Cumulative frequency is: * A) Decreasing * C) Both A and B * **B) Increasing** * D) Relative frequency 20. If B₁ = 0, the distribution is: * A) Positively skewed * C) Negatively skewed * B) Symmetrical * D) Leptokurtic 21. If ẞ2 < 3 the distribution is: * A) Mesokurtic * C) Platykurtic * B) Leptokurtic * D) Symmetrical 22. S.D (y + a) = ____: * A) SD (y) + a * C) SD(y) * **B) |a|SD(y)** * D) a²SD (y) ### Short Questions 1. Given Ef = 120, Efx = 296 and mode = 2.944, comment on the skewness. 2. X of 200 items is 48 and their S² is 9. Find EX of ΣΧ². 3. Define Inter Quartile Range and Quartile Deviation. 4. Define coefficient of variation. What are its uses? 5. Define the moment ratios ẞ1 and ẞ2. For what purposes these are computed? 6. Draw the shapes of meso-turtle, platy-kurtic and lepto kurtic curves. 7. Define the range. How will you calculate it for grouped data? 8. Given that Q1 = 89 and Q.D. = 10.875, then find the value of Q3. 9. Define variance and give its at-least two formulas. 10. For a set of un-grouped values, the following sums are found: n = 15, Σx = 480, Ex² =15735, find the C.V. 11. For a certain distribution mean = 40, median = 41 and coefficient of skewness = - 0.25, find the value of S.D. 12. If var (x) =5 and var f(y) = 1/3, then find var (2x-3y)? 13. If the value of Q2, D5 and P50 are equal to 72.32 then find the median of the distribution? 14. Write four relative measures of dispersion. 15. Explain any two properties of standard deviation. Differentiate symmetry, and skewness. 16. If variance of the value of "X" is 25, what is the standard deviation of X? 17. Explain the moments about mean. 18. Distinguish between positive and negative skewness with diagrams. 19. In a symmetrical distribution, Q1 = 25 and Q3 = 75 then find the value of median. 20. The first two moments of a distribution about X=10 are 2 and 20. Find coefficient of variation.. 21. Define the term 'standard deviation'. 22. Name the various absolute measures of dispersion. 23. Given Mean = 50, Median = 48 and standard deviation = 6 then find Karl's Pearson's coefficient of skewness. 24. What is meant by skewness and how it is calculated? 25. What are the types of dispersion? 26. What is quartile deviation? 27. What is the use of coefficient of variation? 28. What do you say about the relative dispersion of 5. 5, 5.5? 29. 'What do you know about kurtosis? 30. If ẞ2 = 3 and m4 = 1875, then what will be the standard deviation? 31. Define quartiles, also write down its formulae. 32. Define frequency distribution. 33. Write the name of methods used for measures of dispersion. 34. Write any two advantages of the range. 35. Write any two properties of standard deviation. 36. Given that mean = 156.17, median = 153.50 and standard deviation is 19.03. Calculate coefficient of skewness. 37. If S.D(X)=10, then find the standard deviation of the values of 5X. 38. What is meant by relative measure of dispersion? 39. Define mean deviation. 40. Give two properties of variance. 41. If S² = 36 and X = 18, what is coefficient of variation? 42. Define skewness. ### Long Questions 1. From the following data, find combined mean and combined standard deviation: n₁ = 50 X1 = 63 S₁ = 9; n2 = 40 X2 = 54 S2 = 6. 2. The first four moments of a set of numbers about the value 3 are -2, 10, -25, and 50. Determine the first four moments about mean. 3. Find coefficient of quartile deviation from the following data: Group 9.3-9.7 9.8-10.2 10.3-10.7 10.8-11.2 11.3-11.7 F 2 6 10 7 3 4. For a moderately skewed distribution, the mean price is Rs. 20 and the median price is Rs. 17 If the coefficient of variation is 20% find the coefficient of skewness of the distribution? 5. Calculate the first four moments about X = 17.5 from Classes 5-9 10-14 15-19 20-24 25-29 Frequency 5 8 12 10 5 6. Find quartile deviation from the following observations: 10, 12, 15, 25, 28, 35, 42, 20, 32, 18, 14, 5 7. Calculate first four moments about Mean for the following set: 45, 32, 37, 46, 39, 36, 41, 48 and 36.. 8. The ungrouped data is given below. Calculate the Mean Deviation from mean. Data: 2, 5, 6, 6, 8, 9, 12, 13, 16, 23 9. The deviation from X=22.5 of different values of 'X' are: -12, -8.5, 3.0, 0, 2.5, 6.6, 9.2. 1.6, 0.5 and 0.4 Find out lower quartile of X. 10. The first three moments of a distribution about the value 2 are 1,8 and 20. Find (i) variance (ii) is the distribution positively skewed or negatively skewed? 11. Consider the following data. Find coefficient of skewness. Classes 40-50 50-60 60-70 70-80 80-90 F 4 8 16 8 4 12. Compute the variance from the following data: Classes 10-19 20-29 30-39 40-49 50-59 F 5 25 5 40 10 13. If Q2 = 26.01, Q3 = 38.29 Q1 = 13.73 find coefficient of skewness? 14. Calculate coefficient of variation if (i) n=150 Σ(Χ - 100) = 180 and (ii) Σ(Χ - 100)² = 245320. 15. Following are the heights (cms) of 5 students, measured at the time of registration. Compute mean deviation about mean and mean coefficient of dispersion. Heights (cms): 88.03, 94.50, 94.90, 95.50, 84.60 16. The first three moments of a distribution about the value 2 of a variable X, are 1,16 and -40. Show that the mean is 3, variance is 15 and third moment about mean m3 is -86. ## Chapter 05: Index Numbers ### Multiple Choice Questions 1. If all the values consider equal importance in index number is: * A) Simple * C) Unweighted * **B) Weighted** * D) None of these 2. The index number given by Σρη 40 Σρολο × 100 is: * A) Laspeyre's index * C) Paasche's index * **B) Value index** * D) None of these 3. CPI falls in the category of: * A) A simple index of * C) An inflationary index * **B) An aggregative index** * D) Wholesale price index 4. Which of the following formulas is a price index number? * Σρητο x100 A) Σροφο * Σρηαη x100 B) Σροφη * C) родо Σρηαη x100 * D) All of these 5. If all the values are not of equal importance, the index number is called: * A) Weighted * C) Simple * **B) Unweighted** * D) None of these 6. The general purchasing power of the currency of a country is determined by: * A) Retail price index * B) Volume index * C) Composite index * **D) Wholesale price index** 7. For computing chain index number, we compute: * A) Price relative * C) Weighted indices * **B) Link relative** * D) None of these 8. Which of the following average is most suitable for computing chain index number: * Α) Α.Μ. * C) G.M. * **B) Median** * D) H.M. 9. Index number for the base period is always taken as: * A) One * C) 100 * **B) Zero** * D) 200 10. Laspeyer's index number is: * Σροφο A) Σρηξη * ΣΡπαπ B) ΣΡπο * ΣΡπαπ C) Σροφο * ΣΡπαπ D) ΣΡodο 11. An index number computed for a single commodity is called: * A) Simple index * C) Both A and B * B) Composite index * D) None of these 12. Price of base period is denoted by: * A) Pon * C) Pn * **B) Qon** * D) P. 13. In index number base year should be: * A) First year * C) Last year * **B) Second year** * D) Normal year 14. Laspayre's index number is also named as: * A) Current year weighted * C) Ideal index number * **B) Base year weighted** * D) Simple index number ### Short Questions 1. Define index number. 2. Write the name of three different types of index number. 3. If Laspeyer's Index no. is 108 and Fisher's Index no. is 120, find Paasche's Index number? 4. Explain the selection of the suitable average in W.P.I. 5. Given Epq1= 850 and Ep1q1= 1210. Find Paasche's Price Index number. 6. Define unweighted index number. 7. Differentiate between fixed base method and chain base method. 8. Define volume (quantity) index number. Define link relative and how we calculate it. 9. If Fisher's Ideal Index = 117.84 and Laspeyre's Index = 117.9, then what will be Paashe's Index? 10. Define price index number. 11. Define composite index number. 12. Explain the chain base method. 13. Give any two uses of index numbers. 14. If Epoq = 322; Ep1q0 = 340; Ep1q1 = 362 and Epoq1 = 326. Find Fisher's Price Index number? 15. Define composite index number. 16. Define link relatives. 17. What is consumer price index number? 18. Find the current year weighted index for given data Epnqn = 2260, Epoqn = 2230. 19. If Laspeyre's index number = 105.4 and Paache's index number = 103.2, find the Fisher's index number? 2