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Question
During a medical check-up, the number of heartbeats per minute of 30 patients were recorded and summarized as follows:
| Number of heartbeats per minute |
65 – 68 | 68 – 71 | 71 – 74 | 74 – 77 | 77 – 80 | 80 – 83 | 83 - 86 |
| Number of patients |
2 | 4 | 3 | 8 | 7 | 4 | 2 |
Find the mean heartbeats per minute for these patients, choosing a suitable method.
Solution
Using Direct method, the given data is shown as follows:
| Number of heartbeats per minute |
Number of patients `(f_i)` |
Class mark `(x_i)` | `f_i x_i` |
| 65 – 68 | 2 | 66.5 | 133 |
| 68 – 71 | 4 | 69.5 | 278 |
| 71 – 74 | 3 | 72.5 | 217.5 |
| 74 – 77 | 8 | 75.5 | 604 |
| 77 – 80 | 7 | 78.5 | 549.5 |
| 80 – 83 | 4 | 81.5 | 326 |
| 83 – 86 | 2 | 84.5 | 169 |
| Total | `Ʃf_i = 30` | `Ʃf_i x_i = 2277` |
The mean of the data is given by,
x =`(Ʃ_i f_i x_ i )/(Ʃ_i f_i)`
=`2277/30`
=75.9
Thus, the mean heartbeats per minute for these patients is 75.9.
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