The following table gives the frequency distribution of marks scored by 50 students of class X in mathematics examination of 80 marks. Find the median of the data:

Here, we have grouped 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 = 50

Now, we just need to find the value of n/2. So,

⇒

Now, look up for a value in the cumulative frequency just greater than 25.

We have, 31.

Corresponding to this value of cumulative frequency, we can say that median class is 30 – 40.

That is,

Median class = 30 – 40

∴ we have almost everything we require to calculate median.

Median is given by,

Where,

l = lower limit of the median class = 30

n = Total number of observation (sum of frequencies) = 50

cf = cumulative frequency of the class preceding the median class = 15

f = frequency of the median class = 16

c = class size (class sizes are equal) = 10

Putting the values, l = 30, n/2 = 25, cf = 15, f = 16 and c = 10 in the given formula of median, we get

⇒

⇒

⇒

⇒ Median = 30 + 6.25

⇒ Median = 36.25

Thus, the median of the data is 36.25.