Question

Assume a population of 1,3, and 8. Assume that samples of size n=2 are randomly selected with replacement from the population.

Sample   x1   x2
1   1   1
2   1   3
3   1   8
4   3   1
5   3   3
6   3   8
7   8   1
8   8   3
9   8   8

Find the value of the population standard deviation sigmaσ.

Answer 1

Question asked:

Value of the population standard deviation $\sigma$:

Answer:

Population values: 1, 3, 8

From the given population data, the following Table is calculated:

Population Mean ($\mu$) is given by:

$\mu =\frac{\sum_{i=1}^{3}x_{i}}{3}=\frac{12}{3}=4$

x	x - $\mu$	(x - $\mu$)2
1	- 3	9
3	- 1	1
8	4	16
Total =		26

Population Standard Deviation ($\sigma$) is given by:

Σǐel (ri-μ)2 /26 = V8.6667= 2.9439

So,

Answer is:

2.9439