Question

Find the mean deviation from the median of the distribution :
24, 33, 15, 35, 29, 38, 5

Answer 1

Hello!!

dear here is ur answer;!

24, 33, 15, 35, 29, 38, 5

The above observations can be arranged in ascending order as : 5, 15, 24, 29, 33, 35, 38

Here,
n = 7

.°. Median = ( n + 1/ 2 )th observation.

= ( 7 + 1/2 ) th observation.

= 4th observation.

= 29

.°. M.D.

= { | 5 - 29 | + | 15 - 29 | + | 24 - 29 | + | 29 - 29 | + | 33 - 29 | + | 35 - 29 | + | 39 - 29 | } / 7

= ( 24 + 14 + 5 + 0 + 4 + 6 + 9 )/7

= 62/7

= 8.857 ( approx. )

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Answer 2

Mean deviation :
Given, 24, 33 , 15, 35 , 29, 38 , 5
step 1 :- find mean of this observation ,
mean( X) = sum of observations/total number of observation
= ( 24 + 33 + 15 + 35 + 29 + 38 + 5)/7
= 179/7

step 2 :- find absolute value of the diffence between mean and observations .
e.g
|X - X₁ |= 179/7 - 24 = 11/7
|X - X₂| = |179/7 -33| = 52/7
|X - X₃| = 74/7
|X - X₄| = 56/7
|X - X₅| = 24/7
|X - X₆| = 87/7
|X - X₇| = 144/7

step 3 :- find mean of it . result is known as mean deviation
M.D = (11/7 + 52/7 + 74/7 + 56/7 + 24/7 + 87/7 + 144/7 )/7
= (11 + 52 + 74 + 56 + 24 + 87+ 144)/49
= 9.14

madian :
step 1 : - arrange in inceasing order of obsevation .
e.g 5 , 15, 24 , 29 , 33, 35, 38
because number of ohsevations (n) = 7{odd number }
so, medain = (n+1)/2 th term
= (7+1)/2 th term
= 4th term
= 29
hence, median = 29