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Thirty women were examined in a hospital by a doctor and the number of heartbeats per minute were recorded and summarized as follows. Find the mean heart beats 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 women 2 4 3 8 7 4 2


Answer :

From the given data, let us assume the mean as A = 75.5
Class size (h) = 3

So, \(u_i \ = \ \frac{x_i \ - \ A}{h} \ \)
\( \Rightarrow \ u_i \ = \ \frac{x_i \ - \ 75.5}{h} \)

Class Interval Number of women ( \( f_i \) ) Mid-point ( \(x_i \) ) \(u_i \ = \ \frac{x_i \ - \ 75.5}{h} \) \( f_i u_i \)
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 3 8
83-86 2 84.5 3 6
\( \sum f_i \ = 30 \) \( \sum f_i u_i \ = 4 \)

\( \overline{x} \ = \ A \ + h \frac{ \sum \ f_i x_i}{ \sum f_i} \)

\(= 75.5 \ + \ 3 \ × \ \frac{4}{30} \ \)
\( = \ 75.5 \ + \ \frac{4}{10} \ \)
\( = \ 75.9 \)

\(\therefore \) The mean heart beats per minute for these women is 75.9

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