Question

the average estimated hours a person in the united states spent playing video games per year from 2002 to 2012 were 71, 80, 82, 78, 80, 91, 107, 121, 125, 131, and 142. use the statistics calculator to find the variance and population standard deviation. round answers to the nearest whole number. the variance of this data set is. the population standard deviation for this data set is.

Explanation:

Step1: Input data into calculator

Input the data set \(75, 80, 82, 78, 80, 91, 107, 121, 125, 131, 142\) into a statistics calculator.

Step2: Calculate variance

Using the formula for population variance \(\sigma^{2}=\frac{\sum_{i = 1}^{N}(x_{i}-\mu)^{2}}{N}\), where \(N\) is the number of data points and \(\mu\) is the population mean. The calculator gives the variance.

Step3: Calculate standard deviation

Using the formula \(\sigma=\sqrt{\sigma^{2}}\), where \(\sigma^{2}\) is the population variance. The calculator gives the population standard deviation.

Answer:

The variance of this data set is \(700\).
The population standard deviation for this data set is \(26\).