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Problem: mean deviation about median {{10-20,20-30,30-40,40-50,50-60},{15,25,20,12,8}} [ Calculator, Method and examples ]

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Your problem -> mean deviation about median {{10-20,20-30,30-40,40-50,50-60},{15,25,20,12,8}}

 Class(1) f(2) cf(3) Mid value (x)(4) |x-M|=|x-30|(5) f*|x-M|(6)=(2)xx(5) 10 - 20 15 15 15 15 225 20 - 30 25 40 25 5 125 30 - 40 20 60 35 5 100 40 - 50 12 72 45 15 180 50 - 60 8 80 55 25 200 --- --- --- --- --- --- -- n=80 -- -- -- sum f*|x-M|=830

To find Median Class
= value of (n/2)^(th) observation

= value of (80/2)^(th) observation

= value of 40^(th) observation

From the column of cumulative frequency cf, we find that the 40^(th) observation lies in the class 30 - 40.

:. The median class is 30 - 40.

Now,
:. L = lower boundary point of median class =30

:. n = Total frequency =80

:. cf = Cumulative frequency of the class preceding the median class =40

:. f = Frequency of the median class =20

:. c = class length of median class =10

Median M = L + (n/2 - cf)/f * c

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