Question

below are the jersey numbers of 11 players randomly selected from a football team. find the range, variance, and standard deviation for the given sample data. what do the results tell us?
51 26 29 23 55 39 63 79 16 65 53
range = 63 (round to one decimal place as needed.)
sample standard deviation = 20.2 (round to one decimal place as needed.)
sample variance = (round to one decimal place as needed.)

Explanation:

Step1: Recall the formula for sample variance

The formula for sample variance \(s^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}\), where \(n\) is the sample size, \(x_{i}\) are the data points, and \(\bar{x}\) is the sample mean. Another formula is \(s^{2}=s\times s\), where \(s\) is the sample standard deviation.

Step2: Calculate the sample variance

Given that the sample standard deviation \(s = 20.2\).
Using the formula \(s^{2}=s\times s\), we substitute \(s = 20.2\) into the formula.
\(s^{2}=(20.2)\times(20.2)\)
\(s^{2}=408.04\approx408.0\)

Answer:

\(408.0\)