Question

The mean shoe size of the students in a math class is 7.5. Most of the shoe sizes fall within 1 standard deviation, or between a size 6 and a size 9.
What is the standard deviation of the shoe size data for the math class?
A.1.5
B.2.7
C.3.0
D.3.8

Answer 1

The formula of standard deviation is 
SD = square root of (variance)

Variance is the average of the squared differences from the Mean.
Variance = (6-7.5)^2 + (9-7.5)^2 / 2
Variance = 2.25

SD = square root (2.25)
SD = 1.5

The correct answer is A. 1.5

Answer 2

Answer: Option A. 1.5

Mean shoe size of the students in a math class: µ=7.5
Standard deviation: σ
Most of the shoe sizes (x) fall within 1 standard deviation:
µ-1σ<x< µ+1σ

µ-σ<x< µ+σ

or between a size 6 and a size 9:
6<x<9

Comparing µ-σ<x< µ+σ with6<x<9:
µ-σ=6 or µ+σ=9

Replacing µ=7.5 above:
7.5-σ=6 or 7.5+σ=9

Solving for σ:
7.5-σ-7.5=6-7.5 or 7.5+σ-7.5=9-7.5
-σ=-1.5 or σ=1.5
σ=1.5 or σ=1.5
Then σ=1.5