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?
\[
\begin{array}{llllllllllll}
15 & 38 & 45 & 65 & 76 & 9 & 21 & 25 & 77 & 48 & 13 & \text { 믜 }
\end{array}
\]
Range $=\square($ Round to one decimal place as needed. $)$

Step 1 ：First, we arrange the data in ascending order: 9, 13, 15, 21, 25, 38, 45, 48, 65, 76, 77.

Step 2 ：The range is the difference between the largest and smallest values, which is \(77 - 9 = 68\).

Step 3 ：To find the variance, we first need to calculate the mean of the data. The mean is the sum of all the values divided by the number of values, which is \(\frac{9 + 13 + 15 + 21 + 25 + 38 + 45 + 48 + 65 + 76 + 77}{11} = 39.36\) (rounded to two decimal places).

Step 4 ：Next, we subtract the mean from each value, square the result, and then find the average of these squared differences. This gives us the variance. The calculations are as follows: \((9-39.36)^2, (13-39.36)^2, (15-39.36)^2, (21-39.36)^2, (25-39.36)^2, (38-39.36)^2, (45-39.36)^2, (48-39.36)^2, (65-39.36)^2, (76-39.36)^2, (77-39.36)^2\). The sum of these values is 4874.91. Dividing this by the number of values (11) gives us the variance, which is \(\frac{4874.91}{11} = 443.17\) (rounded to two decimal places).

Step 5 ：The standard deviation is the square root of the variance, which is \(\sqrt{443.17} = 21.05\) (rounded to two decimal places).

Step 6 ：The range, variance, and standard deviation are measures of dispersion in the data. The range of 68 tells us that the jersey numbers are spread out over a range of 68. The variance of 443.17 tells us how much the jersey numbers vary from the mean. The standard deviation of 21.05 is another measure of how much the jersey numbers vary from the mean, but it is in the same units as the original data (as opposed to the variance, which is in squared units).