Question

the maximum throwing speeds of pitchers on one team are shown in the table.
maximum pitching speed(mph)
75
60
63
51
45
48
the mean of the data set shown in the table is 57. what is the mean absolute deviation?
6
9
9.5
12

Explanation:

Step1: Find absolute deviations

For each data point \( x \), calculate \( |x - \text{mean}| \). Mean is 57.

• \( |75 - 57| = 18 \)
• \( |60 - 57| = 3 \)
• \( |63 - 57| = 6 \)
• \( |51 - 57| = 6 \)
• \( |45 - 57| = 12 \)
• \( |48 - 57| = 9 \)

Step2: Sum the absolute deviations

Sum these values: \( 18 + 3 + 6 + 6 + 12 + 9 = 54 \)

Step3: Calculate mean absolute deviation

Divide the sum by the number of data points (6): \( \frac{54}{6} = 9 \)

Answer:

9