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Question
The data on the number of patients attending a hospital in a month are given below. Find the average (mean) number of patients attending the hospital in a month by using the shortcut method. Take the assumed mean as 45. Give your answer correct to 2 decimal places.
| Number of patients | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 |
| Number of Days | 5 | 2 | 7 | 9 | 2 | 5 |
Solution
| Number of patients | Number of Days (fi) |
Mid-value xi |
Assumed Mean A= 45 ∴ d= xi -A |
fi × di |
| 10 - 20 | 5 | 15 | -30 | -150 |
| 20 - 30 | 2 | 25 | -20 | -40 |
| 30 - 40 | 7 | 35 | -10 | -70 |
| 40 - 50 | 9 | 45 | 0 | 0 |
| 50 - 60 | 2 | 55 | 10 | 20 |
| 60 - 70 | 5 | 65 | 20 | 100 |
| Total | 30 | -140 |
Mean = `A + (sumf_i d_i)/(sum f_i)`
` = 45+ ((-140))/30 = 45 - 14/3`
`= (135-14)/3 = 121/3`
` = 40.33`
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