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Question
Find the variance and standard deviation of the wages of 9 workers given below:
₹ 310, ₹ 290, ₹ 320, ₹ 280, ₹ 300, ₹ 290, ₹ 320, ₹ 310, ₹ 280
Solution
Arrange in ascending order we get,
280, 280, 290, 290, 300, 310, 310, 320 and 320
Assumed mean = 300
| xi | di = xi − A = xi − 300 |
di2 |
| 280 | − 20 | 400 |
| 280 | − 20 | 400 |
| 290 | − 10 | 100 |
| 290 | − 10 | 100 |
| 300 | 0 | 0 |
| 310 | 10 | 100 |
| 310 | 10 | 100 |
| 320 | 20 | 400 |
| 320 | 20 | 400 |
| `sum"d"_"i"` = 0 | `sum"d"_"i"^2` = 2000 |
Here n = 9, `sum"d"_"i"` = 0, `sum"d"_"i"^2` = 2000
variance = `sum ("d"_"i"^2)/"n" - (sum ("d"_"i")/"n")^2`
= `2000/9 - 0`
= 222.222
Variance = 222.222
Standard deviation = `sqrt("Variance")`
= `sqrt(222.222)`
= 14.907
= 14.91
Variance = 222.22
Standard deviation = 14.91
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