Question

Thirty women were examined in a hospital by a doctor and the number of heartbeats per minute were recorded and summarized as follows. Fine the mean heartbeats per minute for these women, choosing a suitable method.

Number of heartbeats per minute	65 - 68	68 - 71	71 - 74	74 - 77	77 - 80	80 - 83	83 - 86
Number of women	2	4	3	8	7	4	2

Answer 1

To find the class mark of each interval (x_i), the following relation is used:

`x_i  = ("Upper class limit + Lower class limit")/2`

Class size, h, of this data = 3

Taking 75.5 as the assumed mean (a), di, u_i, f_iu_i are calculated as follows.

Number of heart beats per minute	Number of women fi	xi	di = xi − 75.5	`u_i = (x_i-75.5)/3`	fiui
65 − 68	2	66.5	− 9	-3	-6
68 − 71	4	69.5	− 6	-2	-8
71 − 74	3	72.5	− 3	-1	-3
74 − 77	8	75.5	0	0	0
77 − 80	7	78.5	3	1	7
80 − 83	4	81.5	6	2	8
83 − 86	2	84.5	9	3	6
Total	30				4

From the table, we obtain

`sumf_i = 30`

`sumf_iu_i = 4`

mean `barx=a+((sumf_iu_i)/(sumf_i))xxh`

`= 75.5 +(4/30) xx 3`

= 75.5 + 0.4 = 75.9

Therefore, the mean beats per minute for these women are 75.9 beats per minute.