Calculate the mean deviation about the median of the following observa

Calculate the mean deviation about the median of the following observation:(i) 22, 24, 30, 27, 29, 31, 25, 28, 41, 42(ii) 38, 70, 48, 34, 63, 42, 55, 44, 53, 47

Answer»

(i) 22, 24, 30, 27, 29, 31, 25, 28, 41, 42

To calculate the Median (M), let us arrange the numbers in ascending order.

Median is the middle number of all the observation.

22, 24, 25, 27, 28, 29, 30, 31, 41, 42

Here the Number of observations are Even then Median = (28 + 29)/2 = 28.5

Median = 28.5 and n = 10

By using the formula to calculate Mean Deviation,

MD = 1/n ∑ⁿ_i=1|d_i|

MD = 1/n ∑ⁿ_i=1|d_i|

= 1/10 × 47

= 4.7

∴ The Mean Deviation is 4.7.

(ii) 38, 70, 48, 34, 63, 42, 55, 44, 53, 47

To calculate the Median (M), let us arrange the numbers in ascending order.

Median is the middle number of all the observation.

34, 38, 43, 44, 47, 48, 53, 55, 63, 70

Here the Number of observations are Even then Median = (47 + 48)/2 = 47.5

Median = 47.5 and n = 10

By using the formula to calculate Mean Deviation,

MD = 1/n ∑ⁿ_i=1|d_i|

MD = 1/n ∑ⁿ_i=1|d_i|

= 1/10 × 84

= 8.4

∴ The Mean Deviation is 8.4.