are the scores that Jenna has received on her seven quizzes: 16, 13, 20, 16, 12, 17, 18 What is the standard deviation rounded to the nearest tenth?

Answer 1

Formula for standard deviation S_x:

S_x = √(∑ⁿ_{i =1}(x_i - x_m)²/(n - 1))

x_i - the individual term in the series

x_m - Mean

n - number of terms

Writing the series in ascending order:

12, 13, 16, 16, 17, 18, 20

Calculating the sum:

12 + 13 + 16 + 16 + 17 + 18 + 20 = 112

Calculating Mean:

112/7 = 16

x_m = 16

Calculating differences of each term and Mean:

12 - 16 = -4

13 - 16 = -3

16 - 16 = 0

16 - 16 = 0

17 - 16 = 1

18 - 16 = 2

Calculating squares of differences:

16, 9, 0, 0, 1, 4

Adding squares of differences:

16 + 9 + 0 + 0 + 1 + 4 = 30

Divide Sum of squares by "n -1":

n = 7 - 1 = 6 (number of terms is "7")

30 ÷ 6 = 5

Taking square root:

√5 ≅ 2.2

Answer: Standard Deviation is 2.2