Mathematics
Find the mean for the following distribution by short cut method:
| Numbers | Cumulative Frequency |
|---|---|
| 60 | 8 |
| 61 | 18 |
| 62 | 33 |
| 63 | 40 |
| 64 | 49 |
| 65 | 55 |
| 66 | 60 |
Measures of Central Tendency
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Answer
We construct the following table as under taking the assumed mean, a = 63.
| xi | Cumulative frequency | fi | Deviation (di = xi - a) | fidi |
|---|---|---|---|---|
| 60 | 8 | 8 | -3 | -24 |
| 61 | 18 | 18 - 8 = 10 | -2 | -20 |
| 62 | 33 | 33 - 18 = 15 | -1 | -15 |
| 63 | 40 | 40 - 33 = 7 | 0 | 0 |
| 64 | 49 | 49 - 40 = 9 | 1 | 9 |
| 65 | 55 | 55 - 49 = 6 | 2 | 12 |
| 66 | 60 | 60 - 55 = 5 | 3 | 15 |
| Total | 60 | -23 |
Mean = = 62.62.
Hence, the mean of the following distribution is 62.62.
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