Time spent on television by adults and kids are shown in the double dot plot. The mean average deviation (MAD) of the two samples are

14 and 13.4

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12 and 14

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11 and 13

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Solution

The correct option is A 14 and 13.4
The data set from sample 1 is

30, 30, 40, 40, 40, 50, 60, 60, 70, 80

Mean deviation = sum of absolute values of deviations from ‘a’ $\div$ number of observations, where 'a' is the mean of the data.

Mean = $\frac{s u m o f a l l d a t a}{n u m b e r o f d a t a}$

Mean of the data = $\frac{30 + 30 + 40 + 40 + 40 + 50 + 60 + 60 + 70 + 80}{10}$

= $\frac{500}{10}$

= 50

Mean deviation = $\frac{| 30 - 50 | + | 30 - 50 | + | 40 - 50 | + | 40 - 50 | + | 40 - 50 | + | 50 - 50 | + | 60 - 50 | + | 60 - 50 | + | 70 - 50 | + | 80 - 50 |}{10}$

= $\frac{20 + 20 + 10 + 10 + 10 + 10 + 10 + 20 + 30}{10}$

= $\frac{140}{10}$

= 14

The data set in sample 2 is

40, 40, 50, 50, 60, 60, 60, 80, 80, 90

Mean = $\frac{s u m o f a l l d a t a}{n u m b e r o f d a t a}$

Mean of the data = $\frac{40 + 40 + 50 + 50 + 60 + 60 + 60 + 80 + 80 + 90}{10}$

= $\frac{610}{10}$

= 61

Mean deviation = $\frac{| 40 - 61 | + | 40 - 61 | + | 50 - 61 | + | 50 - 61 | + | 60 - 61 | + | 60 - 61 | + | 60 - 61 | + | 80 - 61 | + | 80 - 61 | + | 90 - 61 |}{10}$

= $\frac{21 + 21 + 11 + 11 + 1 + 1 + 1 + 19 + 19 + 29}{10}$

= $\frac{134}{10}$

= 13.4

Hence, the MAD of sample 1 and 2 are 14 and 13.4 respectively.

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