Introduction to Statistics — Unit test Answers

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1
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The five-number summary for the lengths of songs, in minutes, performed by a popular music group is given below.Minimum: 1.8 Q1: 3.3 Median: 3.8 Q3: 4.5 Maximum: 9.2 What is the IQR for the distribution of song lengths?

A
0.5
B
0.7
C
1.2
D
1.5
3

The histogram represents boiling temperatures, in degrees Celsius, of tap water and of a saltwater mix.The median boiling temperature of the tap water is 100°C. The median boiling temperature of the salt water is 102°C. Which statement about the means is most likely true?

Question illustration
A
The mean of the tap water boiling temperatures is about 4° less than the mean of the saltwater boiling temperatures.
B
The mean of the tap water boiling temperatures is about 2° less than the mean of the saltwater boiling temperatures.
C
The mean of the tap water boiling temperatures is about 1° greater than the mean of the saltwater boiling temperatures.
D
The mean of the tap water boiling temperatures is about 3° less than the mean of the saltwater boiling temperatures.
6

John has taken six quizzes in his statistics class. His scores on these quizzes are listed below. 71, 75, 76, 80, 85, 87

A
The new mean will be 82.0 and the new median will be 78.0.
B
The new mean will be 82.0 and the new median will be 80.0.
C
The new mean will be 89.5 and the new median will be 78.0.
D
The new mean will be 89.5 and the new median will be 80.0.
7

Which statements are true about the data used to create the histogram? Select three options.

A
The mean is the best comparison of the measures of center.
B
The juniors tended to have higher essay scores than the sophomores.
C
The medians of both data sets are equal.
D
The interquartile range is the best comparison of the measure of variability.
E
A histogram is the best way to show that both distributions are nearly symmetric.
8

The distribution of the salaries at a small business is strongly skewed with many people making very modest salaries and a few making very large salaries. Which measure of center, mean or median, is a better indication of a "typical” salary at this business?

A
The mean is better because it is not affected by the high salaries.
B
The median is better because it is not affected by the high salaries.
C
It cannot be determined without knowing the actual salaries.
D
Either one would be a good measure of a typical salary because they are the same value.
12

The distribution of ages of runners in a marathon is approximately normal. The oldest participant was 80 and the youngest was 13. Which of the following statements is true of the mean and median ages of the runners?

A
The mean is less than the median.
B
The mean is greater than the median.
C
The mean and median are approximately equal.
D
The actual ages of all runners are needed to decide.
15

The boxplot below displays the arm spans for 44 students.

Question illustration
A
Approximately 75% of the arm spans are less than 180 cm.
B
Approximately 50% of the arm spans are less than 168 cm.
C
Approximately 25% of the arm spans are less than 180 cm.
D
Approximately 75% of the arm spans are greater than 162 cm.
17

Twelve people were surveyed and asked how many people live in their residence. The results are summarized in the table below.

Question illustration
A
The median is 2 people per residence.
B
The median is 2.5 people per residence.
C
The median is 2.8 people per residence.
D
The median is 3.5 people per residence.
18

Test scores for 26 students in an introductory statistics course are displayed in the stemplot below. The scores range from 72 to 98.

Question illustration
A
She could choose either one because they are equal.
B
She should report the mean because it will be greater than the median.
C
She should report the median because it will be greater than the mean.
D
All the missing scores are needed in order to decide.
19

IQ scores are collected from a sample of 36 students at a large university. The scores are summarized in the histogram below.

Question illustration
A
The mean is equal to the median IQ.
B
The mean is less than the median IQ.
C
The mean is greater than the median IQ.
D
It cannot be determined because we cannot tell the exact values of the IQ scores in the sample.

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