Measures of Center and Location Answers

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3

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.
4

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.
5

The scores for 21 students on an exam are summarized in the stemplot below.

Question illustration
A
The mean and median will both increase.
B
Neither the mean nor the median will change.
C
The mean will increase but the median will decrease.
D
The mean will increase but the median will be unchanged.
6

The histogram below shows the number of points scored by a high school basketball team over two seasons.

Question illustration
A
He should report the mean.
B
He should report the median.
C
He could report either because they are equal.
D
The exact number of points per game are needed to decide.
7

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.
8

In some gymnastics meets, the score given to a gymnast is the mean of the judges’ scores after the highest and lowest scores have been tossed out. Nikita’s scores on the floor routine from all of the judges are shown below.7.50, 7.50, 7.75, 7.75, 8.00, 8.00, 8.00, 10.00

A
Her score does not change.
B
Her score is lower after removing the highest and lowest scores.
C
Her score is higher after removing the highest and lowest scores.
D
There is not enough information to determine if her score increases or decreases.

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