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? 37 8 65 76 21 96 46 19 75 72 58 ti 84

Mean = 52.09

The range is 88

Variance = 433. 44

Standard Deviation= s= 20.82

Step-by-step explanation:

The mean is obtained by adding all the values and dividing the number values .

Mean = 37+ 8 +65+ 76 +21 +96+ 46 +19 +75+ 72+ 58+ 84/12

Mean = 573/11 = 52.09

The mean gives the average value .

Range is the difference between the highest and smallest value. The highest value is 96 and lowest value is 8

96 - 8 = 88

The range is 88.

The range gives an idea of the spread of values between two points.

The variance can be calculated by

∑x²=  1369+ 64+ 4225+ 5776+ 441+ 9216+ 2116+ 361+  5625+ 5184+ 3364=  37741

S²= ∑x²/n - ( ∑x/n)²

   =    ∑37741/ 11 - (52.09)²

      = 3431 - 2997.56 = 433. 44

Standard deviation is the square root of the variance

s= √433. 44= 20.82

The large value of standard deviation implies that the observations are scattered widely about the mean. A smaller value indicates that the observations in data set are close to mean.