Answer:
[tex](a)\ \bar x =20.5[/tex]
[tex](b)\ \sigma = 14.54[/tex]
Step-by-step explanation:
Given
[tex]x: 36, 14, 21, 39, 11, 2[/tex]
Solving (a): The mean of the 6 samples.
This is calculated as:
[tex]\bar x = \frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x =\frac{36+ 14+ 21+ 39+ 11+ 2}{6}[/tex]
[tex]\bar x =\frac{123}{6}[/tex]
[tex]\bar x =20.5[/tex]
Solving (b): The sample standard deviation.
This is calculated using:
[tex]\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}[/tex]
So, we have:
[tex]\sigma = \sqrt{\frac{(36 - 20.5)^2 + (14 - 20.5)^2 + (21 - 20.5)^2 + (39 - 20.5)^2 + (11 - 20.5)^2 + (2 - 20.5)^2}{6-1}}[/tex]
[tex]\sigma = \sqrt{\frac{1057.5}{5}}[/tex]
[tex]\sigma = \sqrt{211.5}[/tex]
[tex]\sigma = 14.54[/tex]
