Find the median from following frequency distribution:

Class	0-100	100-200	200-300	300-400	400-500	500-600
Frequency	64	62	84	72	66	52

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 = 400

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 200.

We have, 210.

Corresponding to this value of cumulative frequency, we can say that median class is 200 – 300.

That is,

Median class = 200 – 300

∴ we have almost everything we require to calculate median.

Median is given by,

Where,

l = lower limit of the median class = 200

n = Total number of observation (sum of frequencies) = 400

cf = cumulative frequency of the class preceding the median class = 126

f = frequency of the median class = 84

c = class size (class sizes are equal) = 100

Putting the values, l = 200, n/2 = 200, cf = 126, f = 84 and c = 100 in the given formula of median, we get

⇒

⇒

⇒

⇒ Median = 200 + 88.09

⇒ Median = 288.09

Thus, the median of the data is 288.09.