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Problem: median {{1,3},{2,4},{5,10},{6-10,23},{10-20,20},{20-30,20},{30-50,15},{50-70,3},{70-100,2}} [ Calculator, Method and examples ]

Solution:
Your problem -> median {{1,3},{2,4},{5,10},{6-10,23},{10-20,20},{20-30,20},{30-50,15},{50-70,3},{70-100,2}}

 Class(1) Frequency (f)(2) cf(6) 1 3 3 2 4 7 5 10 17 6 - 10 23 40 10 - 20 20 60 20 - 30 20 80 30 - 50 15 95 50 - 70 3 98 70 - 100 2 100 --- --- --- n = 100 -----

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

= value of (100/2)^(th) observation

= value of 50^(th) observation

From the column of cumulative frequency cf, we find that the 50^(th) observation lies in the class 10 - 20.

:. The median class is 10 - 20.

Now,
:. L = lower boundary point of median class =10

:. n = Total frequency =100

:. 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

=10 + (50 - 40)/20 * 10

=10 + (10)/20 * 10

=10 + 5

=15

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