Measures of Center

Given the data set: 3, 7, 7, 2, 5, 10, 8, calculate the mean.

• 5.5

• 6

• 7

• 6.5

Answer explanation

To calculate the mean, sum the numbers: 3 + 7 + 7 + 2 + 5 + 10 + 8 = 42. Then divide by the count of numbers (7): 42 / 7 = 6. Thus, the mean is 6.

Find the median of the following data set: 12, 15, 11, 14, 13.

• 12

• 13

• 14

• 15

Answer explanation

To find the median, first arrange the data in ascending order: 11, 12, 13, 14, 15. The median is the middle value, which is 13 in this case.

Match the following data sets with their modes.

• 2, 3, 6, 6, 6, 7

• 6

• 5, 5, 9, 9, 9, 10

• 8

• 4, 5, 6, 6, 7, 8, 8, 8, 9

• 7

• 1, 2, 3, 7, 7, 7

• 9

Answer explanation

The mode is the number that appears most frequently in a data set. In this case, the number 8 appears three times, more than any other number, making it the mode of the data set.

Match the following data sets with their ranges.

• 10, 22, 14, 26, 18

• 10

• 22, 29, 15, 18, 25

• 7

• 5, 12, 9, 16, 19

• 12

• 3, 8, 13, 18, 23

• 14

Answer explanation

To find the range, subtract the smallest value (15) from the largest value (29). So, 29 - 15 = 14. Therefore, the range of the data set is 14.

The mean absolute deviation of the data set: 5, 10, 15, 10, 5 is (a)  

• 2
• 3
• 4
• 5

Answer explanation

To find the mean absolute deviation, first calculate the mean: (5+10+15+10+5)/5 = 10. Then, find the absolute deviations: |5-10|, |10-10|, |15-10|, |10-10|, |5-10| = 5, 0, 5, 0, 5. The mean of these deviations is (5+0+5+0+5)/5 = 2.

Match the following data sets with their means.

• 4, 5, 6, 5, 6, 6

• 7

• 10, 6, 8, 8, 8, 8

• 9

• 9, 3, 6, 3, 9, 12

• 8

• 5, 7, 9, 11, 13, 9

• 6

Answer explanation

To find the mean, sum the numbers: 9 + 3 + 6 + 3 + 9 + 12 = 42. Then divide by the count of numbers (6): 42 / 6 = 7. Thus, the mean is 7.

Find the median of the following data set: 21, 18, 24, 30, 27.

• 21

• 24

• 27

• 30

Answer explanation

To find the median, first arrange the data in ascending order: 18, 21, 24, 27, 30. The median is the middle value, which is 24 in this case.

The mode of the data set 14, 18, 14, 20, 22, 18, 18 is (a)   .

• 14
• 18
• 20
• 22

Answer explanation

The mode is the number that appears most frequently in a data set. In this case, 18 appears three times, more than any other number. Therefore, the mode of the data set is 18.

Calculate the range of the data set: 45, 32, 37, 50, 41.

• 18

• 15

• 13

• 8

Answer explanation

To find the range, subtract the smallest value (32) from the largest value (50). So, 50 - 32 = 18. Therefore, the range of the data set is 18.

The mean absolute deviation of the data set: 2, 4, 6, 8, 10 is (a)   .

• 2
• 3
• 4
• 5

Answer explanation

To find the mean absolute deviation, first calculate the mean: (2+4+6+8+10)/5 = 6. Then, find the absolute deviations: |2-6|=4, |4-6|=2, |6-6|=0, |8-6|=2, |10-6|=4. The mean of these deviations is (4+2+0+2+4)/5 = 2.