123 EDEN 1090/1092 Practice Problems in Measures of Variability Practice 1 1 . The data sets below are the quiz scores of randomly selected students from two different groups that were given the same statistics quiz: Group A: 6, 8, 10, 12, 13, 13, 16, 18, 20 Group B: 12, 15, 15, 17, 19, 19, 20, 22 a. Compute the 5-number summary for each section by filling in the table below. Group Min Q1 Q2 Q3 Max Semi-Interquartile Range A B b. Calculate the range and simi-interquartile range for each section. Group A: Group B: c. Which Group has the higher mid-point for the scores? Justify your answer. d. Which Group has a wider spread in the scores? Justify your answer. 2. A veterinarian is looking at the weight of puppies from the same household in kilograms: 1 , 2, 7, 7. What is the mean? Using Computational Formula Calculate SD: X Ex = E( x 2 ) =124 on average by Interpret the SD: Scores vary from the mean of (SD). ". We randomly selected 6 Gorilla's for all the zoos in southern California. We want to use the ages (in years) of these Gorillas to estimate the parameters for the ages of all Gorillas in South California zoos: 7, 15, 18, 3, 9, 10 What is the mean? Calculate SD: Using Computational Formula x E(x ?) = Interpret the SD: Scores vary from the mean of on average by (SD). 4. Calculate the standard deviation or variance as indicated using the given information. REMEMBER! (Standard Deviation)2 = Variance Variance = Standard Deviation a. Variance = 107.76; Calculate the Standard Deviation. b. Standard Deviation = 73.14; Calculate the Variance.126 5. Use given measurements for groups A, B, and C to answer the following: Group A: X = 6 5 2.5 Group B: a = 10.5 s = 1.25 Group C: x - 8.7 s = 3.2 a. List the Groups in order of the lowest mean to the highest mean. b. List the Groups in order from the lowest variability to highest variability. c. What is the 68%, 95%, and 99.7% range for Group A? d. What is the 68%, 95%, and 99.7% range for group B? 6. Students in Group A have a mean of 6 and standard deviation of 2.5. Students in Group B have a mean of 10.5 and standard deviation of 1.25. Fill in the blanks below. 99.9% 99.7% 95% 68% 0.13% ; 2.14% 13.59% 34.13% 34.13% 13.59% 2.14% * 0.13% +16 #20 130 +40 -46 -20 -10 0 6 Group A 10.5 Group B