5.9

Chapter 5 Exercises

CHAPTER 5: MEASUREMENTS OF VARIABILITY

Name:

izzle.co

External data sets, such as data set #2 and #7 need for this chapter, can be found at:

http://www.3ringpublishing.com/csu/csv.html.

1. The mean and the median are measures of center. The standard deviation is a measure of spread that uses

the mean in the calculation. The mean and the standard deviation are commonly used together to measure

the center and spread of symmetric data sets. The median is an appropriate way to measure the center of a

skewed distribution. Explain why it makes sense to use the 5 number summary to measure the spread of a

skewed distribution rather than the standard deviation.

2.

Consider the sample data 2, 4, 6, 5, 27, 10, 3, 8.

2:3, 4, 516, 9,10,271,

X 825

(a) Report the mean and median. Which of these two measurements of location would you choose to describe

this data set, and why? Be sure to label each value using the appropriate symbol.

ex, = (2+that quot;+27+10+71= (8:25)

8-8

0= 7.545%

(b) Report the range, variance and standard deviation. Be sure to label the variance and standard deviation

min2

using the appropriate symbol.

Q= 3.

red. s

min = 2

3. ) Consider the sample data 9, 11, 15, 13, 7, 12, 8.

(a) Report the mean and median. Which of these two measurements of location would you choose to describe

this data set, and why? Be sure to label each value using the appropriate symbol.

(b) Report the range, variance and standard deviation. Be sure to label the variance and standard deviation

using the appropriate symbol.

4.) Both the standard deviation and variance can never take on a negative value. Explain why.Statistics and Probability