Thirty women were examined in a hospital by a doctor and the number of heart beats per minute recorded and summarized as follows. Find the mean heart beats per minute for these women, choosing a suitable method.
Number of heart beats 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 |
Find the mean of each of the following frequency distributions: (5-14)
We may find class mark of each interval (xi) by using the relation.
xi =
Class size of this data = 3
Now taking 75.5 as assumed mean (A), we may calculate di, ui, fiui as following:
No. of heart beat per minute | Number of women (fi) | xi | di = xi – 75.5 | ui = | fiui |
65 – 68 | 2 | 66.5 | -9 | -3 | -6 |
68 – 71 | 4 | 69.5 | -6 | -2 | -8 |
71 – 74 | 3 | 72.5 | -3 | -1 | -3 |
74 – 77 | 8 | 75.5 | 0 | 0 | 0 |
77 – 80 | 7 | 78.5 | 3 | 1 | 7 |
80 – 83 | 4 | 81.5 | 6 | 2 | 8 |
83 – 86 | 2 | 84.5 | 9 | 3 | 6 |
N = 30 | ∑fiui = 4 |
Now we may observe from table that ∑fi = 30, ∑fiui = 4
Mean (X̅) = di + * h
= 75.5 + * 3
= 75.5 + 0.4 = 75.9
So mean of heart beat per minute of women are 75.9 beats per minute.