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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