Question

The following table shows the ages of the patients admitted in a hospital during a year.
Age (in years): 5-15 15-25 25-35 35-45 45-55 55-65
No. of students: 6 11 21 23 14 5
Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

Answer 1

We may compute class marks ($x_i$ )as per the relation

Now taking 30 as assumed mean (a) we may calculate $d_i$ and $f_i{d}_i$ as follows.

Age (in years)	Number of patients$f_i$	Class marks xi	$d_i=x_i-275$	$f_i{d}_i$
5 – 15	6	10	-20	-120
15 – 25	11	20	-10	-110
25 – 35	21	30	0	0
35 – 45	23	40	10	230
45 – 55	14	50	20	280
55 – 65	5	60	30	150
Total	80			430

From the table, we may observe that

Clearly, mean of this data is 35.38. It represents that on an average the age of patients admitted to hospital was 35.38 years.

As we may observe that maximum class frequency is 23 belonging to class interval 35 – 45

So, modal class = 35 – 45

Lower limit (l) of modal class = 35

Frequency (f) of modal class = 23

Class size (h) = 10

Frequency ($f_1$) of class preceding the modal class = 21

Frequency ($f_2$) of class succeeding the modal class = 14

Clearly, the mode is 36.8. It represents that the maximum number of patients admitted in the hospital was of age 36.8 years.