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?
85 42 11 2 61 12 46 10 47 29 8
range = 83 (round to one decimal place as needed )
sample standard deviation = 26.4 (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.
We know that the sample standard deviation \(s = 26.4\)

Step2: Use the relationship between variance and standard deviation

The relationship between sample variance \(s^{2}\) and sample standard deviation \(s\) is \(s^{2}=(s)^{2}\)

Substitute \(s = 26.4\) into the formula: \(s^{2}=(26.4)^{2}\)

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Answer:

\(697.0\)