Question

2In a moderately symmetric distribution if the difference of the mode
and the median is 24, then the difference of the median and mean is
(a) 12
(b) 24
(c) 10
(d) 6​

Answer 1

Given :

Symmetric distribution in which difference between mode & median is 24

i.e. mode - median = 24

To Find :

Difference between median & mean

i.e. median - mean = ?

Given options are

(a) 12

(b) 24

(c) 10

(d) 6​

Solution :

•We know that ,

mean = 1/2( 3 median - mode )

2 mean = 3 median - mode

_________________(1)

•It is given that ,

mode - median = 24

mode = 24 + median

_______________(2)

• Putting (2) in (1)

2 mean = 3 median - ( 24 + median )

2 mean = 3 median - 24 - median

2 mean = 2 median - 24

24 = 2 median - 2 mean

24 = 2 ( median - mean )

median - mean = 24/2

median - mean = 12

• Hence difference between median and mean is 12

so , option A is correct