Answer:
[tex]\sigma = 0.831[/tex] --- Standard deviation
[tex]Mode = 10[/tex]
Step-by-step explanation:
Given
[tex]x = 9,8,10,9,8,10,9,10,8,10[/tex]
Solving (a): The population standard deviation
First, we calculate the mean
[tex]\bar x = \frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x = \frac{9+8+10+9+8+10+9+10+8+10}{10}[/tex]
[tex]\bar x = \frac{91}{10}[/tex]
[tex]\bar x = 9.1[/tex]
The standard deviation is:
[tex]\sigma = \sqrt{\frac{1}{n}\sum (x - \bar x)^2}[/tex]
So, we have:
[tex]\sigma = \sqrt{\frac{1}{10}*[(9 - 9.1)^2+.................+(10- 9.1)^2]}[/tex]
[tex]\sigma = \sqrt{\frac{1}{10}*6.9}[/tex]
[tex]\sigma = \sqrt{0.69}[/tex]
[tex]\sigma = 0.831[/tex]
The mode is:
[tex]Mode = 10[/tex]
10 has the highest frequency of 4
