below are the jersey numbers of 11 players randomly selected from a football team. find the range, variance…

Explanation:

Step1: Identify the data set

The data set is (37,31,6,65,94,33,82,38,86,91,0)

Step2: Calculate the range

The range is the difference between the maximum and minimum values. Maximum value (= 94), minimum value (= 0). Range (=94 - 0=94)

Step3: Calculate the mean (\bar{x})

(\bar{x}=\frac{37 + 31+6+65+94+33+82+38+86+91+0}{11}=\frac{563}{11}\approx51.2)

Step4: Calculate the squared - differences ((x_i-\bar{x})^2) for each data point (x_i)

For (x_1 = 37): ((37 - 51.2)^2=(-14.2)^2 = 201.64) For (x_2 = 31): ((31 - 51.2)^2=(-20.2)^2 = 408.04) For (x_3 = 6): ((6 - 51.2)^2=(-45.2)^2 = 2043.04) For (x_4 = 65): ((65 - 51.2)^2=(13.8)^2 = 190.44) For (x_5 = 94): ((94 - 51.2)^2=(42.8)^2 = 1831.84) For (x_6 = 33): ((33 - 51.2)^2=(-18.2)^2 = 331.24) For (x_7 = 82): ((82 - 51.2)^2=(30.8)^2 = 948.64) For (x_8 = 38): ((38 - 51.2)^2=(-13.2)^2 = 174.24) For (x_9 = 86): ((86 - 51.2)^2=(34.8)^2 = 1211.04) For (x_{10}=91): ((91 - 51.2)^2=(39.8)^2 = 1584.04) For (x_{11}=0): ((0 - 51.2)^2=(-51.2)^2 = 2621.44)

Step5: Calculate the variance (s^2)

(s^2=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}) (\sum_{i = 1}^{11}(x_i-\bar{x})^2=201.64+408.04 + 2043.04+190.44+1831.84+331.24+948.64+174.24+1211.04+1584.04+2621.44 = 11345.6) (s^2=\frac{11345.6}{10}=1134.6)

Step6: Calculate the standard deviation (s)

(s=\sqrt{s^2}=\sqrt{1134.6}\approx33.7)

Answer:

33.7