Question

Find the median of the following frequency distribution: Weekly wages (in Rs.)           60-69                  70-79     80-89     90-99                  100-109 110-119 No. of days:             5             15                  20           30           20                  8

Answer 1

In this question, total frequency`(N)` = `5+15+20+30+20+8 = 98`
So,`N/2 = 49`
If, we calculate cumulative frequency that is equal to or just greater than `49`, it comes `70`, making `90-99` our median class.
As, `70` is the less than type cumulative frequency corresponding to the class boundary `89.5`
So, lower class boundary`(l) = 89.5`
Cumulative frequency of the class preceding the median class`(F) = 40`
Frequency of median class`(f) = 30`
Interval`(i) = 10`
We know, Median =` (l+((N/2)-F)/f)**i`
Putting above values in formula,
Median = `89.5+((49-40)/30)**10`
`= 89.5+9**10/30`
`Median = 89.5+3 = 92.5`