Question -
Answer -
First we have to writethe first 10 multiples of 3,
3, 6, 9, 12, 15, 18,21, 24, 27, 30
So, x̅ = (3 + 6 + 9 +12 + 15 + 18 + 21 + 24 + 27 + 30)/10
= 165/10
= 16.5
Let us make the tableof the data and append other columns after calculations.
| Xi | Deviations from mean (xi – x̅) | (xi – x̅)2 |
| 3 | 3 – 16.5 = -13.5 | 182.25 |
| 6 | 6 – 16.5 = -10.5 | 110.25 |
| 9 | 9 – 16.5 = -7.5 | 56.25 |
| 12 | 12 – 16.5 = -4.5 | 20.25 |
| 15 | 15 – 16.5 = -1.5 | 2.25 |
| 18 | 18 – 16.5 = 1.5 | 2.25 |
| 21 | 21 – 16.5 = – 4.5 | 20.25 |
| 24 | 24 – 16.5 = 7.5 | 56.25 |
| 27 | 27 – 16.5 = 10.5 | 110.25 |
| 30 | 30 – 16.5 = 13.5 | 182.25 |
| | 742.5 |
Then, Variance
= (1/10) × 742.5
= 74.25
∴Mean = 16.5 andVariance = 74.25