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### Problems: Measuring Dispersion 2

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9. From this sample data find the mean, median, mode, variance, and standard deviation: 8, 13, 11, 9, 9.

10. Compute as many measures of dispersion as you can for the following numbers: 3, 6, 6, 7, 5, 3.

11. You have a sample of seven items. You have computed the mean, and the following are six of the deviations from the mean: 3. 3. -2. -1. 0. -1. What is the variance of this sample?

12. John likes numbers so much that he counts just about everything. He has been counting how many people have been in front of him when he goes to the post office. For the last 8 visits, this is what he found: 0, 1, 4, 2, 0, 3, 0, 2.

a) Compute the mean, median, and mode of these data.
b) Compute the range and standard deviation. (Show how you get the answer.)

13. An office supply company has a fleet of 10 trucks that are used for making local deliveries. During a recent month, the number of miles each truck was driven were as follows:

 Truck Miles driven (x 100) 1 23 2 34 3 20 4 18 5 30 6 30 7 30 8 38 9 25 10 27

Compute the following descriptive measures:

a) mean
b) median
c) mode
d) range
e) variance
f) sample standard deviation

14. Answer the next questions using these two sets of numbers:

Data Set #1: 3, 4, 5, 9, 10, 11
Data Set #2: 2, 6, 6, 7, 14

a) Which of these two data sets has the higher center as measured by the median? Explain.
b) Which of these two data sets has the higher center as measured by the mean? Explain.
c) Which of these two data sets has more variability as measured by the range? Explain.
d) Which of these two data sets has more variability as measured by the variance? Explain, showing your computations.
e) Which of these two data sets has more variability as measured by the standard deviation? Explain.

15. From this sample data find the mean, median, mode, variance, and standard deviation: 10, 11, 0, 3, 8, 8, 9.

16. I went bowling a while back, and in the first five frames I got the following scores: 8, 1, 9, 8, 9.

a) What is the average score for these five frames?
b) What is the median score for these five frames?
c) Statisticians talk about the root mean square. To find the root mean square of a list of numbers, you square each number, then find the mean of them, and finally take the square root. Subtract the average from each of the numbers above and find the root mean square.
d) In part c you have just computed the ________________ of a population.
e) Now subtract the median form each of the scores and compute the root mean square. Is it larger or smaller than the answer you got in part c?

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