Premium Online Home Tutors
3 Tutor System
Starting just at 265/hour

# 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

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