Question

The data representing a random sample of 15 people playing soccer and basketball is shown below

From the given data, MAD (soccer) is MAD (basketball).

• A. less than
• B. greater than
• C. equal to

Answer 1

The correct option is A less than

For people playing soccer:

Sum of data values = 12 + 21 + 40 + 27 + 20 = 120
Number of data values = 15

$\text{Mean}=\frac{\text{Sum of data values}}{\text{Number of data values}}=\frac{120}{15}$ = 8

Sum of absolute deviation = 14

$\text{MAD(soccer)}=\frac{\text{Sum of absolute deviation}}{\text{Number of data values}}$

$=\frac{14}{15}=0.93$

For people playing basketaball:

Sum of data values =4 + 10 + 18 + 21 + 24 + 18 + 10 = 105
Number of data values = 15

$\text{Mean}=\frac{\text{Sum of data values}}{\text{Number of data values}}=\frac{105}{15}$ = 7

Sum of absolute deviation = 20

$\text{MAD(Basketball)}=\frac{\text{Sum of absolute deviation}}{\text{Number of data values}}$

$=\frac{20}{15}=1.33$

Hence, MAD (soccer) is less than MAD (basketball).