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

To find the class mark (\(x_i\)) for each interval, the following relation is used.  

Class mark  \((x_i)\) = \(\frac {\text{Upper \,limit + Lower \,limit}}{2}\)

class size (h) of the data =  3 

Taking 75.5 as assumed mean (a), \(d_i\), \(u_i\), and \(f_iu_i\) can be calculated as follows.   

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

From the table, it can be observed that  

\(\sum f_i = 30\)
\(\sum f_iu_i = 4\)

Mean, \(\overset{-}{x} = a + (\frac{\sum f_iu_i}{\sum f_i})h\) 

x = \(75.5 + (\frac{4 }{30}) \times 20\) 

x = 75.5 - \((\frac{4}{30}) \times 3\) 

x = 75.5 + 0.4

x = 75.9

Therefore, mean hear beats per minute for these women are 75.9 beats per minute.