91影视

The jersey numbers of a sample of 11 players are given.

The number of observations $\left(n\right)$ is 11.

Different statistical values are calculated to identify the amount of dispersion/variation present in the data. Some of them are as follows:

Range: It tells the overall expanse of the data. It is calculated as the difference between the lowest values and the highest value.

Variance: It is the average value of the square of the deviations of the individual values from the mean $\left(\stackrel{炉}{x}\right)$. The formula of the sample variance is

$s^2=\frac{{鈭�}_{1=1}^n{\left(x_i-\stackrel{炉}{x}\right)}^2}{n-1}$

Standard deviation: It is defined as the square root of the computed variance.

The range is calculated as

.$$\begin{gathered} \text{Range}=\text{Maximum}\text{Value}-\text{Minimum}\text{Value} \\ =99-7 \\ =92.0 \end{gathered}$$

Therefore, the range of the jersey numbers is equal to 92.0.

The mean of the sample is calculated as

$$\begin{gathered} \stackrel{炉}{x}=\frac{{鈭�}_{1=1}^n{x}_i}{n} \\ =\frac{89+91+...+60}{11} \\ =\frac{628}{11} \\ 鈮�57.1 \end{gathered}$$

.

Thus, the mean of the sample is 57.1.

The sample variance $\left(s^2\right)$ is calculated as

$$\begin{gathered} s^2=\frac{{鈭�}_{1=1}^n{\left(x_i-\stackrel{炉}{x}\right)}^2}{n-1} \\ =\frac{{\left(89-57.1\right)}^2+{\left(91-57.1\right)}^2+...+{\left(60-57.1\right)}^2}{11-1} \\ =\frac{11494.909}{10} \\ 鈮�1149.5 \end{gathered}$$

Therefore, the variance of the jersey numbers is equal to 1149.5.

The sample standard deviation $\left(s\right)$is equal to

$$\begin{gathered} s=\sqrt{s^2} \\ =\sqrt{1149.5} \\ 鈮�33.9 \end{gathered}$$

Therefore, the standard deviation of the jersey numbers is equal to 33.9.

As the jersey numbers are a form of categorical data, any mathematical measure for this data has no significance. Thus, the values of range, standard deviation, and variance have no meaning.