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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