Question

The following table shows the number of patients of different age group 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)	Number of Patients Discharged (f i )	Class Marks (xi )	xi f i
5-15	6	10	60
15-25	11	20	220
25-35	21	30	630
35-45	23	40	920
45-55	14	50	700
55-65	5	60	300
Total	80		\(\Sigma\)xifi = 2830

Shaded Class is Modal Class.

\(\therefore\)   Mean of Data = \(\frac{\Sigma x_i f_i}{\Sigma f_i}= \frac{2830}{80}\)

= 35.375

And Mode = I + \(\left(\frac{f_0-f_1}{2f_0-f_1-f_2}\right)\)× h, where I = 35, f₀ =23, f₁ = 21, f₂ = 14 and h = 10.

\(\therefore\) Mode of Data = 35 + \(\left(\frac{23-21}{2×23-21-14} \right)× 10\)

= \(35+\frac{20}{11}\)

= \(\frac{405}{11}\)

= 36.82 (approx.)