Question

which data set is the most spread from its mean?
14, 26, 24, 28
22, 16, 18, 36
22, 28, 20, 22
21, 19, 27, 25

Explanation:

To determine which data set is most spread from its mean, we calculate the mean absolute deviation (MAD) for each set. MAD is the average of the absolute differences between each data point and the mean.

Step 1: Calculate the mean for each data set

• First set: 14, 26, 24, 28

Mean $= \frac{14 + 26 + 24 + 28}{4} = \frac{92}{4} = 23$

• Second set: 22, 16, 18, 36

Mean $= \frac{22 + 16 + 18 + 36}{4} = \frac{92}{4} = 23$

• Third set: 22, 28, 20, 22

Mean $= \frac{22 + 28 + 20 + 22}{4} = \frac{92}{4} = 23$

• Fourth set: 21, 19, 27, 25

Mean $= \frac{21 + 19 + 27 + 25}{4} = \frac{92}{4} = 23$

Step 2: Calculate MAD for each set

• First set: |14 - 23| + |26 - 23| + |24 - 23| + |28 - 23|

$= 9 + 3 + 1 + 5 = 18$
MAD $= \frac{18}{4} = 4.5$

• Second set: |22 - 23| + |16 - 23| + |18 - 23| + |36 - 23|

$= 1 + 7 + 5 + 13 = 26$
MAD $= \frac{26}{4} = 6.5$

• Third set: |22 - 23| + |28 - 23| + |20 - 23| + |22 - 23|

$= 1 + 5 + 3 + 1 = 10$
MAD $= \frac{10}{4} = 2.5$

• Fourth set: |21 - 23| + |19 - 23| + |27 - 23| + |25 - 23|

$= 2 + 4 + 4 + 2 = 12$
MAD $= \frac{12}{4} = 3$

The second set (22, 16, 18, 36) has the highest MAD (6.5), so it is most spread from its mean.

Answer:

B. 22, 16, 18, 36