Find the mean and variance for the first 10 multiples of 3
The first 10 multiples of 3 are 3,6,9,12,15,18,21,24,27,30
Here number of observation are n=10
∴ Mean,¯X=∑10i=1xi10=16510=16.5
Now,
xi
| (Xi−¯X) | (Xi−¯X)2 |
3 | -13.5 | 182.25 |
6 | -10.5 | 110.25 |
9 | -7.5 | 56.25 |
12 | -4.5 | 20.25 |
15 | -1.5 | 2.25 |
18 | 1.5 | 2.25 |
21 | 4.5 | 20.25 |
24 | 7.5 | 56.25 |
27 | 10.5 | 110.25 |
30 | 13.5 | 182.25 |
|
| 742.5 |
∴
Variance (σ2)=1n10∑i=1(Xi−¯X)2=110×742.5=74.25