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Question:

Thirty women were examined in a hospital by a doctor and the number of heart beats per minute were recorded and summarised as follows. Find the mean heart beats per minute for these women, choosing a suitable method. Number of heart beats 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

Solution:

Class interval Mid value(xi)(fi)ui=xi−75.53fiui
65–68 66.5 2 -3 -6
68–71 69.5 4 -2 -8
71–74 72.5 3 -1 -3
74–77 75.5 8 0 0
77–80 78.5 7 1 7
80–83 81.5 4 2 8
83–86 84.5 2 3 6
Total 30 4
Lets take assumed mean,A as 75.5
Class interval=3
∴ui=xi−Ah=xi−75.53
̄x=A+h∑fiui∑fi=75.5+3×430=75.5+0.4=75.9
Hence, the mean heart beats per minute for these women is 75.9