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 from the mean.

Step 1: Calculate mean for each data set

• Set 1: 14, 26, 24, 28

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

• Set 2: 22, 16, 18, 36

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

• Set 3: 22, 28, 20, 22

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

• Set 4: 21, 19, 27, 25

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

Step 2: Calculate absolute deviations from mean

• Set 1: |14-23|, |26-23|, |24-23|, |28-23|

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

• Set 2: |22-23|, |16-23|, |18-23|, |36-23|

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

• Set 3: |22-23|, |28-23|, |20-23|, |22-23|

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

• Set 4: |21-23|, |19-23|, |27-23|, |25-23|

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

Step 3: Compare MAD values

Set 2 (22, 16, 18, 36) has the highest MAD (6.5), so it is most spread from its mean.

Answer:

B. 22, 16, 18, 36