Question

The following are all 5 quiz scores of a student in a statistics course. Each quiz was graded on a 10-point scale.6, 8, 9, 6, 5,Assuming that these scores constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places.

Answer 1

For this type of problem we use the following formula:

`\begin{gathered} \sigma=\sqrt[]{\frac{\sum^{}_{}(x_i-\mu)^2}{N},} \\ \\ \end{gathered}`

where μ is the population mean, xi is each value from the population, and N is the size of the population.

First, we compute the population mean in order to do that we use the following formula:

`\mu=(\Sigma x_i)/(N)\text{.}`

Substituting each value of x_i in the above formula we get:

`\mu=(6+8+9+6+5)/(5)=(34)/(5)=6.8.`

Now, we compute the difference of each x_i with the mean:

`\begin{gathered} 6-6.8=-0.8, \\ 8-6.8=1.2, \\ 9-6.8=2.2, \\ 6-6.8=-0.8, \\ 5-6.8=-1.8. \end{gathered}`

Squaring each result we get:

`\begin{gathered} (-0.8)^2=0.64, \\ (1.2)^2=1.44, \\ (2.2)^2=4.84, \\ (-0.8)^2=0.64, \\ (-1.8)^2=3.24. \end{gathered}`

Now, we add the above results:

`0.64+1.44+4.84+0.64+3.24=10.8.`

Dividing by N=5 we get:

`(10.8)/(5)=2.16.`

Finally, taking the square root of 2.16 we obtain the standard deviation,

`\sigma=\sqrt[]{2.16}\approx1.47.`

Answer:

`\sigma=1.47.`