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

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Solution

Here, we have

sum from blank to blank of straight f equals space 30 comma space space sum from blank to blank of straight f subscript straight i straight u subscript straight i equals 4 comma space

A (assumed mean) = 75.5 and h =3
Now,

top enclose straight x space equals space A plus fraction numerator begin display style sum from blank to blank of end style f subscript i u subscript i over denominator begin display style sum from blank to blank of end style f subscript i end fraction x h equals 75.5 plus 4 over 30 x 3 equals 75.5 plus 4 over 10 equals 75.5 plus 0.4 equals 75.9

Hence, the mean heart beats per minute is 75.9.

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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