Question

Calculate the range, population variance, and population standard deviation for the following data if necessary round to one more decimal place.

Answer 1

Step 1

Given;

Required;

Step 2

The range is the difference between the biggest data and the smallest data.

`32-4=28`

Population variance is a measure of the spread of population data. Hence, population variance can be defined as the average of the distances from each data point in a particular population to the mean squared, and it indicates how data points are spread out in the population. It is given as;

The population variance will be;

`\begin{gathered} Mean=10 \\ Population\text{ variance=56.6} \end{gathered}`

Step 3

Population standard deviation looks at the square root of the variance of the set of numbers. It's used to determine a confidence interval for drawing conclusions (such as accepting or rejecting a hypothesis). A slightly more complex calculation is called sample standard deviation.

It is given by;

`Population\text{ standard deviation }\approx\text{7.5233}`

Answer;

`\begin{gathered} Range=28 \\ Population\text{ variance=56.6} \\ Popukation\text{ standard deviation}\approx7.5\text{ to 1 decimal places} \end{gathered}`