The following table shows the ages of the patients admitted in a

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 + $[\frac{(f_1 - f_0)}{(2f_1 - f_0 - f_2)}]$ x h

Here,

L = lower class limit of modal class = 35

$f_1$ = frequency of modal class = 23

$f_0$ = frequency of class proceeding to modal class = 21

$f_2$ = 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 + $[\frac{(f_1 - f_0)}{(2f_1 - f_0 - f_2)}]$ x h

= 35 + $[\frac{(23 - 21)}{(2 \times 23 - 21 - 14)}]$ x 10

= 35 + $(\frac{2}{11})$ x 10

= 35 + $\frac{22}{11}$ = 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 = $L+ \left [\frac{\frac{n}{2}-c_f}{f}\right] \times h$