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	Σfi = 30			Σfidi = –140

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

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

= `45 - 14/3`

= `(135-14)/3`

= `121/3`

= 40.33