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?

20 82 57 94 44 28 46 15 49 55 34

Answer 1

Variance: 589.0545454545456

Standard Deviation: 24.270445926157716

Range: 79

Explanation:

First, I added up all of the numbers:15 + 20 + 28 + 34 + 44 + 46 + 49 + 55 + 57 + 82 + 94 = 524

I squared the total, and then divided the number of items in the data set524 x 524 = 274576

274576 / 11 = 24961.454545454544

I took my set of original numbers from step 1, squared them individually this time, and added them all up:(15 x 15) + (20 x 20) + (28 x 28) + (34 x 34) + (44 x 44) + (46 x 46) + (49 x 49) + (55 x 55) + (57 x 57) + (82 x 82) + (94 x 94) = 30852

I subtracted the amount in step 2 from the amount in step 3:30852 - 24961.454545454544 = 5890.545454545456

I subtracted 1 from the number of items in my data set:11 - 1 = 10

I divided the number in step 4 by the number in step 5:5890.545454545456 / 10 = 589.0545454545456

This is my Variance!

Finally, I took the square root of the number from step 6 (the Variance),

√(589.0545454545456) = 24.270445926157716

This is my Standard Deviation!