Questions: Calculate the range, population variance, and population standard deviation for the following data set. If necessary, round to one more decimal place than the largest number of decimal places given in the data. 13,13,13,13,13,13,13,13,13,13 Range: Population Variance: Population Standard Deviation:

Solution Steps

The range of a data set is calculated by subtracting the smallest value from the largest value. For the given data set:

\[ \text{Range} = \max(13, 13, 13, 13, 13, 13, 13, 13, 13, 13) - \min(13, 13, 13, 13, 13, 13, 13, 13, 13, 13) = 13 - 13 = 0 \]

The mean of a data set is the sum of all data points divided by the number of data points. For the given data set:

\[ \text{Mean} = \frac{13 + 13 + 13 + 13 + 13 + 13 + 13 + 13 + 13 + 13}{10} = \frac{130}{10} = 13 \]

The population variance is the average of the squared differences between each data point and the mean. For the given data set:

\[ \text{Population Variance} = \frac{(13-13)^2 + (13-13)^2 + \ldots + (13-13)^2}{10} = \frac{0}{10} = 0 \]

The population standard deviation is the square root of the population variance. For the given data set:

\[ \text{Population Standard Deviation} = \sqrt{0} = 0 \]

Final Answer