Question

Find the median of the following data: (2) Class interval Frequency 0-10 5 10-20 8 20-30 23 30-40 17 40-50 7 50-60 8

Answer 1

We prepare the cumulative frequency table, as given below:

Class                                    :   0-10   10-20   20-30   30-40  40-50  50-60

Frequency(f)                        :    5       8          23         17          7        8     N = 68

Cumulative frequency (cf) :    5       13         36         53        60       68

We have to find, the median of the given data.

Solution:

Here, N = 68

∴ $\dfrac{N}{2} =\dfrac{68}{2}$ = 34

The cumulative frequency just greater than 34 is 36 and the correspondence class is 20-30.

Thus, the medial class = 20-30

l = 20, h = 10, f = 23, cf = 13 and  = $\dfrac{N}{2} =\dfrac{68}{2}$ = 34

Median =$l+\dfrac{(\dfrac{N}{2} -cf)}{f} \times h$

= $20+\dfrac{(34 -13)}{23} \times 10$

= $20+\dfrac{21}{23} \times 10$

= 20 + 9.13

= 29.13

Thus, the median of the given data is "equal to  29.13".