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?
○ 1.5
○ 2.7
○ 3.0
○ 3.8

Explanation:

Step1: Recall 1 standard deviation rule

A value within 1 standard deviation of the mean lies in the interval $\text{Mean} - \text{Standard Deviation}$ to $\text{Mean} + \text{Standard Deviation}$.

Step2: Set up equations from given range

We know $\text{Mean} = 7.5$, lower bound $=6$, upper bound $=9$.
For the lower bound: $7.5 - \sigma = 6$
For the upper bound: $7.5 + \sigma = 9$

Step3: Solve for standard deviation $\sigma$

From the lower bound equation:
$\sigma = 7.5 - 6 = 1.5$
Verify with upper bound:
$\sigma = 9 - 7.5 = 1.5$

Answer:

1.5