**Q) The following table shows the ages of the patients admitted in a hospital during a year:**

Find the mode and mean of the data given above.

**Ans: **

**(i) Mode value of the data:**

Since the modal class is the class with the highest frequency.

In the given question, class “35 – 45” has 23 frequency which is the highest frequency among all other classes.

**Hence, modal class is “35 – 45”.**

Now mode of the grouped data is calculated by:

Mode = L + x h

Here,

L = lower class limit of modal class = 35

_{ }= frequency of modal class = 23

_{ }= frequency of class proceeding to modal class = 21

_{ }= frequency of class succeeding to modal class = 14

h = class size = 45 – 35 = 10

Let’s put values in the formula and solve:

Mode = L + x h

= 35 + x 10

= 35 + x 10

= 35 + =** 36.82**

**Hence, the mode value is 36.82**

**(ii) Median value of data:**

To calculate the median value, let’s re-organize the data:

To find the median, we need to first identify middle class of the data.

- We know that, Median class is the class where the cumulative frequency crosses 50% of total of frequencies.
- Here, in the given data, total of frequencies is 80 and at row 4 cumulative frequency is crossing 50% of total (i.e. 40)
- Hence, our Median class = 35 – 45

Next, the median value of a grouped data is given by:

Median =

Here:

L = Lower boundary of the median class = 35

n = Total number of frequencies = 80

= Cumulative frequency of the class before the median class = 38

f = Frequency of the median class = 23

h = Class width = 45 – 35 = 10

hence, the Median =

⇒ 35 + [(40 – 38)] x

⇒ 35 + =** 35.87**

**Therefore, Median value of the grouped data is 35.87**

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