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?
$\begin{array}{llllllllllll}2 & 6 & 47 & 27 & 14 & 71 & 69 & 35 & 73 & 94 & 34 & \square\end{array}$
Range $=\square$ (Round to one decimal place as needed.)
The range tells us that the jersey numbers span from 2 to 94. The variance and standard deviation tell us that the jersey numbers are quite spread out from the mean, with a standard deviation of 29.03. This means that on average, each jersey number is about 29.03 units away from the mean.
Step 1 :Given the jersey numbers of 11 players randomly selected from a football team are: \(2, 6, 47, 27, 14, 71, 69, 35, 73, 94, 34\).
Step 2 :The range is the difference between the highest and lowest values in the dataset. To find the range, we first sort the data in ascending order and then subtract the smallest value from the largest value.
Step 3 :The variance is a measure of how much values in the dataset vary. To calculate the variance, we first find the mean (average) of the dataset. Then, for each number in the dataset, we subtract the mean and square the result. The variance is the average of these squared differences.
Step 4 :The standard deviation is a measure of how spread out the numbers in the data are. It is simply the square root of the variance.
Step 5 :By calculating, we find that the range of the data is \(92\), the variance is approximately \(842.63\), and the standard deviation is approximately \(29.03\).
Step 6 :Final Answer: The range of the jersey numbers is \(\boxed{92}\). The variance is \(\boxed{842.63}\) (rounded to two decimal places). The standard deviation is \(\boxed{29.03}\) (rounded to two decimal places).
Step 7 :The range tells us that the jersey numbers span from 2 to 94. The variance and standard deviation tell us that the jersey numbers are quite spread out from the mean, with a standard deviation of 29.03. This means that on average, each jersey number is about 29.03 units away from the mean.