PRII Statistics for Research II PDF

Practical Research Practical Research Practical Research Practical Research Practical Research Practical Research Basic Statistics:...

Practical Research Practical Research Practical Research Practical Research Practical Research Practical Research Basic Statistics: Practical Research COMPUTATION Karen Collins Ramos Practical Research  Practical Research 01 Practical Research CHECK Practical Research Practical Research Practical Research Practical Research Practical Research Practical Research Question 1 It is a single value that attempts to describe a set of data by identifying the central position within a set of data. A. Measures of central tendency B. Measures of dispersion C. Measures of shape Question 2 It is the sum of the measures divided by the number of measures in a variable. A. Mean B. Median C. Mode Question 3 It is the value with the greatest frequency A. Mean B. Median C. Mode Question 4 It is the middle entry or term in a set of data in either increasing or decreasing order A. Mean B. Median C. Mode Question 5 Which is the correct means to compute for the range? A. The sum of the largest and smallest number B. The number in the middle C. The difference between the largest and smallest number D. The number that appears most often Question 6 What is an outlier? A. The difference between the greatest and least numbers in a data set B. The mean of the distances from each data value in a set to the mean of a set C. The difference between the upper and lower quartiles of a data set D. A value that is much less or much greater than the other values in a data set Question 7 Which is the correct means to compute for the range? A. The sum of the largest and smallest number B. The number in the middle C. The difference between the largest and smallest number D. The number that appears most often Question 8 What does the standard deviation represent? A. How many different variations are there in the data set B. How spread out each data value is from the mean C. How the population varies compared to the sample D. The range, but with other variables in consideration Question 9 The data below share the same mean. A. Set 1 Standard Deviation = 3.1 B. Set 2 Standard Deviation = 4.9 C. Set 3 Standard Deviation = 1.7 D. Set 4 Standard Deviation = 3.2 Which set of data probably has the points closest to the mean? Question 10 In selecting the most appropriate measure of central tendency, one consideration is the: A. Total number of scores B. The standard deviation C. The range D. The presence of outliers  Practical Research 02 Practical Research SETS Practical Research Practical Research Practical Research Practical Research Practical Research Practical Research MEASURES OF POSITION 01 Mean - Arithmetic average of scores x = Σx/n Middle value of a distribution 02 Median (n + 1)/2 Most frequent value in a data 03 Mode set  What is the mean of the data set below? x- = Σx/n 25 20 17 15 21 24 x- = (25 + 20 + 17 + 15 + 21 + 24) / 6 = 20.33  Compute for the mEAN x- = Σx/n 104 100 120 93 114 107 116 -  Compute for the mEAN x- = Σx/n 39 32 29 32 20 13 -  Compute for the mEAN x- = Σx/n 11 10 14 17 9 6 4 12 19 21 4 2 - 1.B. MEDIAN The middle value where exactly half of the data values are above it and half are below it Less widely used Can reduce effects of outliers Often used when the data is nonsymmetrical  MEDIAN ODD: Arrange the values from smallest to largest and get the middlemost value EVEN: Median = (n + 1)/2 If whole number: keep as is If not a whole number: get the first whole number less than the location value and the first whole number greater than the location value  WHAT IS THE MEDIAN OF THE DATA SET BELOW? 25 20 17 15 21 24 1. Arrange the values from least to greatest: a. 15, 17, 20, 21, 24, 25 b. Solve: (n + 1) / 2, where n is 6 c. (6 + 1) / 2 = 3.5 (not a whole number) d. Get the 3rd and 4th value (20, 21) as the median  What is the MEDIAN of the data set below? 100 120 93 102 114 107 116 93, 100, 102, 107, 114, 116, 120 (n + 1) / 2 (8)/2 = 4 4th value = 107  Compute for the MEDIAN X͂ = 11 10 14 17 9 6 4 12 19 21 4 2 -  Compute for the MEDIAN X͂ = 230 156 167 100 321 199 145 -  Compute for the MEDIAN X͂ = 54 21 16 48 55 24 67 32 - 1.C. MODE The value that occurs the most often in a data set Rarely used as a central tendency measure More useful to distinguish between unimodal and multimodal distributions ○ When the data has more than one peak  What is the MODE of the data set below? 100 120 93 100 114 107 116 ^ X=  What is the MODE of the data set below? 21 23 54 57 76 23 56 45 77 76 23 56 33 27 ^ X=  What is the MODE of the data set below? 11 3 9 5 12 4 3 12 ^ X= 2. MEASURES OF SPREAD The spread refers to how the data deviates from the position measure Gives an indication of the amount of variation in the process Important indicator of the quality of the data Statistics used to describe the spread of the data: Range Standard deviation MEASURES OF SPREAD 1 2 STANDARD RANGE DEVIATION 2.A. RANGE RANGE (R) = Maximum score/data - minimum score/data Ex. 21 23 54 57 76 23 56 45 77 76 23 56 33 27 Max: 77 Min: 21 R = 77 - 21 = 56  What is the RANGE of the data set below? 11 3 9 5 12 4 3 12 R=  What is the RANGE of the data set below? 23 17 12 14 14 11 2 19 21 R=  What is the RANGE of the data set below? 67 34 56 77 45 43 56 68 71 78 45 31 89 65 R= 2.B. Standard Deviation s = standard deviation x bar = mean of the data set x = values of the data set x - x bar = each data point subtracted by the mean n = size of the data set  COMPUTING FOR THE SAMPLE STANDARD DEVIATION Step 1: Get the mean (x-bar) Step 2: Find each score’s deviation from the mean (subtract each score from the mean) Step 3: Square each deviation from the mean Step 4: Find the sum of squares Step 5: Find the variance by dividing the sum of squares by n-1 (sample) Step 6: find the square root of the variance  What is the STANDARD DEVIATION of the data set below? 23 17 12 14 STEP 1: Get the mean (x-bar) Mean = 16.5  What is the STANDARD DEVIATION of the data set below? 23 17 12 14 Step 2: Find each score’s deviation from the mean (subtract each score from the mean) 23-16.5 = 6.5 17-16.5 = 0.5 12 - 16.5 = -4.5 14 - 16.5 = -2.5  What is the STANDARD DEVIATION of the data set below? 23 17 12 14 Step 3: Square each deviation from the mean (6.5)2 = 42.25 (0.5)2 = 0.25 (-4.5)2 = 20.25 (-2.5)2 = 6.25  What is the STANDARD DEVIATION of the data set below? 23 17 12 14 Step 4: Find the sum of squares 42.25 + 0.25 + 0.25 + 6.25 = 69  What is the STANDARD DEVIATION of the data set below? 23 17 12 14 Step 5: Find the variance by dividing the sum of squares by n-1 (sample) N=4 69 / (4-1) = 13  What is the STANDARD DEVIATION of the data set below? 23 17 12 14 Step 6: find the square root of the variance √23 =4.8  What is the STANDARD DEVIATION of the data set below? 23 17 12 14 14 11 2 19 21 s=  What is the STANDARD DEVIATION of the data set below? 68 71 78 45 31 89 65 s=