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Q.

Thirty women were examined in a hospital by a doctor and the number of heart beats per minute were recorded and summarized 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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Detailed Solution

From the given data, let us assume the mean as A = 75.5

x_i= $\frac{u p p e r l i m i t + l o w e r l i m i t}{2}$

Class size (h) = 3

Now, find the u_iand f_iu_i as follows:

Class Interval	Number of women (f_i)	Mid-point (x_i)	u_i = (x_i – 75.5)/h	f_iu_i
65-68	2	66.5	-3	-6
68-71	4	69.5	-2	-8
71-74	3	72.5	-1	-3
74-77	8	75.5	0	0
77-80	7	78.5	1	7
80-83	4	81.5	2	8
83-86	2	84.5	3	6
	Sum f_i= 30			Sum f_iu_i= 4

Mean = x̄ = A + h $\frac{\sum_{} f_{i} u_{i}}{\sum_{} f_{i}}$

= 75.5 + 3× $\frac{4}{30}$

= 75.5 + $\frac{4}{10}$

= 75.5 + 0.4

= 75.9

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

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Thirty women were examined in a hospital by a doctor and the number of heart beats per minute were recorded and summarized as follows. Find the mean heart beats per minute for these women, choosing a suitable method.Number of heart beats per minute65-6868-7171-7474-7777-8080-8383-86Number of women2438742