Find the median for the following:

Value of variable	12	13	14	15	16	17	18	19	20
Frequency	7	10	15	18	20	10	9	8	3

Here, we have ungrouped data given in the table. We need to find cumulative frequency of the data, which will predict our answer.

So,

We have added up all the values of the frequency in the second column and have got,

Total = n = 100

Since, n (=100) is even then the median will be the average of and observations.

We have

⇒

And

⇒

⇒

Note that, in the above table:

50^th observation = 15 &

51^st observation = 16

[∵ 50 and 51 lies between 50 and 70 in the cumulative frequency column]

Taking their average, we get

⇒

⇒

⇒ Median = 15.5

Thus, the median is 15.5