Question

The data on the number of patients attending a hospital in a month are given below. Find the average (mean) number of patients attending the hospital in a month by using the shortcut method.  Take the assumed mean as 45. Give your answer correct to 2 decimal places.

Number of patients	10 -  20	20 - 30	30 - 40	40 - 50	50 - 60	60 -  70
Number of Days	5	2	7	9	2	5

Answer 1

Number of patients	Number of Days (fi)	Mid-value xi	Assumed Mean A= 45 ∴ d= xi -A	fi × di
10  - 20	5	15	-30	-150
20  - 30	2	25	-20	-40
30  - 40	7	35	-10	-70
40 -  50	9	45	0	0
50 -  60	2	55	10	20
60 -  70	5	65	20	100
Total	30			-140

Mean = `A + (sumf_i d_i)/(sum f_i)`

` = 45+ ((-140))/30 = 45 - 14/3`

`= (135-14)/3            = 121/3`

` = 40.33`