Question

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	65 - 68	68 - 71	71 - 74	74 - 77	77 - 80	80 - 83	83 - 86
Number of boxs	2	4	3	8	7	4	2

Answer 1

The class mark (\(x_i\)) for each interval is calculated using the formula: Class mark (\((x_i)\)) = (Upper limit + Lower limit) / 2. The class size (h) for this data is 3. With 75.5 designated as the assumed mean (a), the values for \(d_i\), \(u_i\), and \(f_iu_i\) are determined as shown in the table below.

Number of heart beats per minute	Number of women (\(\bf{f_i}\))	\(\bf{x_i}\)	\(\bf{d_i = x_i -75.5}\)	\(\bf{u_i = \frac{d_i}{3}}\)	\(\bf{f_iu_i}\)
65 - 68	2	66.5	-9	-3	-6
68 - 71	4	69.5	-6	-2	-8
71 -74	3	72.5	-3	-1	-1
74 - 77	8	75.5	-3	-1	-3
77 - 80	7	78.5	3	1	7
80 - 83	7	78.5	3	1	7
83 - 86	2	84.5	9	3	6
Total	30				4

The table shows that \(\sum f_i = 30\) and \(\sum f_iu_i = 4\). The mean (\(\overset{-}{x}\)) is calculated as: \(\overset{-}{x} = a + (\frac{\sum f_iu_i}{\sum f_i})h\). Substituting the values: Mean = \(75.5 + (\frac{4 }{30}) \times 3\). This simplifies to Mean = 75.5 + 0.4, resulting in a mean of 75.9. Therefore, the average heartbeats per minute for these women is 75.9.