Question

The following table shows the number of patients of different age groups who were discharged from the hospital in a particular month:

Age (in years)	Number of Patients Discharged
5 − 15	6
15 − 25	11
25 − 35	21
35 − 45	23
45 − 55	14
55 − 65	5
Total	80

Find the ‘mean’ and the ‘mode’ of the above data.

Answer 1

Age (in years) C.I.	No. of Patients Discharged (f)	Mid value (x)	f.x.
5 − 15	6	10	60
15 − 25	11	20	220
25 − 35	21 → f0	30	630
35 − 45	23 → f1	40	920
45 − 55	14 → f2	50	700
55 − 65	5	60	350
Total	`bb(sumf = 80)`		`bb(sumfx = 2830)`

Mean = `(∑fx)/(∑f)`

= `2830/80`

= 35.38

So, the mean of the given data is 35.38.

Mode:

The maximum frequency is 23, and it corresponds to the 35 – 45 age group.

f₁ = 23, f₀ = 21, f₂ = 14

l = 35, h = 10

Mode = `l + ((f_1 - f_0)/(2f_1 - f_0 - f_2)) xx h`

= `35 + ((23 - 21)/(2 xx 23 - 21 - 14)) xx 10`

= `35 + (2/(46 - 35)) xx 10`

= `35 + 20/11`

= 35 + 1.82

= 36.82

Therefore, the mode of the given data is 36.82.