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Math 243
Review Practice for Test 1
Name: _________________________
Note: This assignment serves as a review exercise for test 1.
1. No computation is needed for this exercise; just eyeball the data sets. Determine whether the first
distribution is more variable than the second or whether the two are equal.
[a] 1, 2, 4, 5, 3 and 9, 7, 4, 2, 0
1st sample
2nd sample
1st sample
[b] 4, 3, 4, 2, 2 and 14, 13, 14, 12, 12
2nd sample
2. Look at the following two sample distributions. Without any calculation (just look over the data
sets), decide which one has the larger standard deviation.
Sample A: 6, 5, 4, 3, 2, 1, 0
Sample B: 6, 6, 6, 0, 0, 0
A
B
3. Consider the following two samples:
Sample A:
7
5
3
Sample B:
107
105
103
1
101
[a] Find the range of each sample.
[b] Calculate the standard deviation of each sample.
[c] What conclusion can you draw about the effect of the size of the numbers on the standard
deviation?
4. Consider the following two samples:
Sample A:
5
8
9
Sample B:
1
4
4
1
6
0
11
10
4
2
5
[a] Find the mean and range of each sample.
[b] By visual inspection, which sample do you think is more variable?
A
B
[c] Check your answer to Part [b] by calculating the standard deviation of each sample.
[d] Does the range or the standard deviation provide a better indication of variability? Explain.
Circle the appropriate response to each question.
1. If 10 is added to each value in a list, the standard deviation is increased by 10.
T
F
2. Add a constant to each number on a list.
A
The mean will change.
B
The standard deviation will change.
3. If the standard deviation of a list is zero, which of the following are correct?
A
The mean is also zero.
B
All the numbers in the list are zero.
C
All the numbers in the list are the same.
D
The median and the mean are the same.
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Math 243
Review Practice for Test 1
4. Suppose you increase each number in a list by 5. The standard deviation will
A
increase
B
decrease
C
stay the same
5. Suppose you increased each number in a list by 50%. The standard deviation would
A
increase by 50%
B
decrease by 50%
C
stay the same
6. Data set A has more variation that data set B. Decide which of the following statements are
necessarily true?
A
Data set A has a larger mean than data set B.
B
Data set A has a larger standard deviation than data set B.
Question 1 (Adapted)
The employees and the management of a company are having a labor dispute. Explain why the
employees might use the median income of all the employees to justify a raise but management use the
mean income to argue that a raise is not needed.
Question 2 (Adapted)
Where do Americans tend to fall on the conservative-liberal political spectrum? The General Social
Survey asks, “I’m going to show you a seven-point scale on which the political views that people
might hold are arranged from extremely liberal, point 1, to extremely conservative, point 7. Where
would you place yourself on this scale?” the table shows the seven-point scale and the distribution of
1331 responses for a recent survey (2002).
Score
Category
Frequency
1
2
3
4
5
6
7
Extremely liberal
Liberal
Slightly liberal
Moderate, middle of road
Slightly conservative
Conservative
Extremely conservative
47
143
159
522
209
210
41
This is a categorical scale with ordered categories, called an ordinal scale. Ordinal scales are often
treated in a quantitative manner by assigning scores to the categories and then using numerical
summaries such as the mean and standard deviation.
[a] Compute the mean of the data.
[b] Identify the mode.
[c] In which category does the median fall? Why?
[d] Parts [a], [b], and [c] showed how to find the mean and median when a categorical variable has
ordered categories. A categorical scale that does not have ordered categories (such as choice of
religious affiliation or choice of major in college) is called a nominal scale. For such a variable, the
mode applies, but not the mean or median. Explain why.
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