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?
$\begin{array}{llllllllllll}5 & 34 & 27 & 60 & 8 & 56 & 69 & 49 & 42 & 13 & 21 & \square\end{array}$
Sample standard deviation $=$
(Round to one decimal place as needed.)
\(\boxed{\text{Final Answer: The range of the data is 64, the variance is 440.1, and the standard deviation is 21.0. This tells us that the data points are quite spread out from the mean.}}\)
Step 1 :Given the jersey numbers of 11 players randomly selected from a football team: \(5, 34, 27, 60, 8, 56, 69, 49, 42, 13, 21\)
Step 2 :First, we calculate the range, which is the difference between the highest and lowest values in the data set. In this case, the range is \(69 - 5 = 64\)
Step 3 :Next, we calculate the variance, which is the average of the squared differences from the mean. The variance for this data set is approximately \(440.1\)
Step 4 :Finally, we calculate the standard deviation, which is the square root of the variance. The standard deviation for this data set is approximately \(21.0\)
Step 5 :These measures tell us about the spread of the data. A high range, variance, or standard deviation indicates that the data points are spread out from the mean, while a low value indicates that they are close to the mean.
Step 6 :\(\boxed{\text{Final Answer: The range of the data is 64, the variance is 440.1, and the standard deviation is 21.0. This tells us that the data points are quite spread out from the mean.}}\)