Calculate the median from the following distribution :
Class                 Frequency 
5-10                         5
10-15                       6
15-20                       15
20-25                       10
25-30                         5
30-35                         4

Dear Student,

Please find below the solution to the asked query:

We form table from given information , As  :

Class	Mid point ( x )	Frequency ( f )	Cumulative frequency Cf
5 - 10	8	5	5
10 - 15	13	6	11
15 - 20	18	15	26
20 - 25	23	10	36
25 - 30	28	5	41
30 - 35	33	4	45
		$\sum _{}$f = 45

fx  = 40 , 78 , 270 , 230 , 140 , 132 $\sum _{}$fx = 890
So,
Mean  = $\frac{{\sum }_{}^{}fx}{{\displaystyle \sum _{}}f}$ = $\frac{890}{{\displaystyle 45}} = \mathbf{19}\mathbf{.}\mathbf{78}$                                                         ( Ans )
And
Median group is  15 - 20  , As we have mean 19.78

And
we know formula for median  = $L +\frac{{\displaystyle \frac{n}{2}} - C{f}_b}{f_m}\times w$
Here

L is the lower class boundary of the median group =  15
n is the total number of data =  45
cf_b is the cumulative frequency of the groups before the median group =  11
f_m is the frequency of the median group = 15
w is the group width =  5
So,
Median  = $15 +\frac{{\displaystyle \frac{45}{2} - 11}}{15}\times 5 = 15 + \frac{22.5 - 11}{15}\times 5 = 15 + \frac{11.5}{15}\times 10= 15 + \frac{115}{15} = \frac{225 +115}{15} = \frac{340}{15} = \mathbf{22}\mathbf{.}\mathbf{67}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{(}\mathbf{ }\mathbf{Ans}\mathbf{ }\mathbf{)}$


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