**Q) **In a hospital the ages of diabetic patients were recorded as follows. Find the median age.

**Ans: **Let’s re-organize the data in the frequency table to find out each part:

To find the median, we need to identify middle value of the data. Let’s rearrange the data:

- First, we need to find the cumulative frequency in the frequency table to find the median. Its shown in last column.
- Next, Total number of sub-divisions or Sum of the frequencies = 140. It shown in the last row of middle column.
- Next, we need to identify Median Class. Since the Median class is the class where the cumulative frequency crosses 50% of the half the total number of sub-divisions, here in the table, Cumulative frequency of 115 is crossing 50% of frequency i.e. 50, at class “45-60”. Hence, our Median class = 45-60
- Next, To find the median, we use the formula:

Median = L+x h

Here:

L = Lower boundary of the median class = 45

n = Total number of sub-divisions = 140

= Cumulative frequency of the class before the median class = 65

f = Frequency of the median class = 50

h = Class width = 60 – 45 = 15

hence, the Median = 45 + x 15

⇒ 45 + [(70 – 65)] x

⇒ 45 +

⇒ 45 + 1.5

⇒ 46.5 years

**Therefore, Median = 46.5 years**