Question
Thirty women were examined in a hospital by a doctor and the number of heart beats per minute were recorded and summarized as follows. Fine 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 |
Solution
To find the class mark of each interval (x_{i}), the following relation is used
`x_i = ("Upper class limit + Lower class limit")/2`
Class size, h, of this data = 3
Taking 75.5 as assumed mean (a), di, u_{i}, f_{i}u_{i} are calculated as follows.
Number of heart beats per minute |
Number of women f_{i} |
x_{i} | d_{i} = x_{i }− 75.5 | u_{i} = d_{i}/3 | f_{i}u_{i} |
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 |
Total | 30 | 4 |
From the table, we obtain
`sumf_i = 30`
`sumf_iu_i = 4`
mean `barx=a+((sumf_iu_i)/(sumf_i))xxh`
`= 75.5 +(4/30) xx 3`
= 75.5 + 0.4 = 75.9
Therefore, mean hear beats per minute for these women are 75.9 beats per minute.
Is there an error in this question or solution?
Solution Thirty women were examined in a hospital by a doctor and the number of heart beats per minute were recorded and summarized as follows Concept: Mean of Grouped Data.