Statistics: Measures of Center and Spread Worksheet

Question 1

Find the mean of this data set: 6, 8, 10, 12, 14.

Accepted Answer

The mean is 10 because the sum is 50 and 50 divided by 5 is 10.

Question 2

Find the median of this data set: 15, 9, 12, 18, 11.

Accepted Answer

The median is 12 because the data in order is 9, 11, 12, 15, 18, and 12 is the middle value.

Question 3

Find the mode of this data set: 4, 7, 7, 9, 10, 10, 10, 12.

Accepted Answer

The mode is 10 because it appears more often than any other value.

Question 4

Find the range of this data set: 23, 18, 31, 25, 20.

Accepted Answer

The range is 13 because the greatest value is 31, the least value is 18, and 31 minus 18 equals 13.

Question 5

A student recorded the number of minutes spent reading each day: 20, 25, 25, 30, 35. Find the mean and median.

Accepted Answer

The mean is 27 minutes because the sum is 135 and 135 divided by 5 is 27. The median is 25 minutes because 25 is the middle value.

Question 6

Find the mean absolute deviation, or MAD, for this data set: 2, 4, 6, 8, 10.

Accepted Answer

The mean is 6. The absolute deviations are 4, 2, 0, 2, and 4, and their mean is 12 divided by 5, so the MAD is 2.4.

Question 7

Find the lower quartile, upper quartile, and interquartile range for this data set: 3, 5, 7, 9, 11, 13, 15.

Accepted Answer

The lower quartile is 5, and the upper quartile is 13. The interquartile range is 8 because 13 minus 5 equals 8.

Question 8

Two data sets have the same mean. Set A is 10, 10, 10, 10, 10. Set B is 2, 6, 10, 14, 18. Which set has the greater spread, and how do you know?

Accepted Answer

Set B has the greater spread because its values are farther apart and its range is 16. Set A has a range of 0 because all values are the same.

Question 9

A basketball player scored 8, 12, 14, 16, and 20 points in five games. What is the mean number of points scored per game?

Accepted Answer

The mean is 14 points per game because the total is 70 points and 70 divided by 5 equals 14.

Question 10

A small data set is 5, 6, 7, 8, 24. Which measure of center, mean or median, better represents a typical value in this data set? Explain.

Accepted Answer

The median better represents a typical value because 24 is much larger than the other values and raises the mean. The median is 7, which is closer to most of the data.

Question 11

The number of pets owned by students in a class is shown here: 0, 1, 1, 2, 2, 2, 3, 4. Find the mean, median, and mode.

Accepted Answer

The mean is 1.875 pets because the sum is 15 and 15 divided by 8 is 1.875. The median is 2 because the middle two values are 2 and 2. The mode is 2 because it appears most often.

Question 12

A data set has a minimum of 12, a lower quartile of 18, a median of 25, an upper quartile of 31, and a maximum of 40. Find the range and interquartile range.

Accepted Answer

The range is 28 because 40 minus 12 equals 28. The interquartile range is 13 because 31 minus 18 equals 13.

Statistics: Measures of Center and Spread

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