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? 14 75 31 23 77 63 88 40 68 11 60 Range=nothing ​(Round to one decimal place as​ needed.)

Answer 1

Answer:

The range is 77.

The variance is 739.8.

The standard deviation is 27.2.

Step-by-step explanation:

The data provided, in ascending order is as follows:

S = {11 , 14 , 23 , 31 , 40 , 60 , 63 , 68 , 75 , 77 , 88}

The range of a data set is the difference between the maximum and minimum values.

From the above data set we know,

Maximum = 88

Minimum = 11

Compute the range as follows:

Range = Maximum - Minimum

           = 88 - 11

           = 77

The range is 77.

Compute the mean of the data as follows:

$\bar x=\frac{1}{n}\sum x_{i}=\frac{1}{11}\times [11+14+23+...+88]=50$

Compute the variance as follows:

$\sigma^{2}=\frac{1}{n-1}\sum (x_{i}-\bar x})^{2}$

    $=\frac{1}{11-1}\times [(11-50)^{2}+(14-50)^{2}+...+(88-50)^{2}]\\\\=\frac{1}{10}\times 7398\\\\=739.8$

The variance is 739.8.

Compute the standard deviation as follows:

$\sigma=\sqrt{\frac{1}{n-1}\sum (x_{i}-\bar x})^{2}}=\sqrt{739.8}=27.199265\approx 27.2$

The standard deviation is 27.2.