Mathematics

Thirty women were examined in a hospital by a doctor and the number of heartbeats per minute were recorded and summarised as follows. Find the mean heartbeats per minute for these women, choosing a suitable method.
Number of heartbeats per minute Number of women
65 - 68 2
68 - 71 4
71 - 74 3
74 - 77 8
77 - 80 7
80 - 83 4
83 - 86 2

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

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We will use step deviation method.

In the following table a is the assumed mean and h is the class size.

Here, h = 3.

By formula,

Class mark = $\dfrac{\text{Upper limit + Lower limit}}{2}$

Number of heartbeats per minute	Number of women (f_i)	x_i	d_i = x_i - a	u_i = (x_i - a)/h	f_iu_i
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	a = 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	Σf_i = 30				Σf_iu_i = 4

By formula,

Mean = a + $\dfrac{Σf$

Substituting values we get :

$\text{Mean } = 75.5 + \dfrac{4}{30} \times 3 \\[1em] = 75.5 + \dfrac{4}{10} \\[1em] = 75.5 + 0.4 \\[1em] = 75.9$

Hence, mean = 75.9

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