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 the property of standard - deviation

In a normal - like distribution (when most data is within 1 standard deviation of the mean), if the mean is $\mu$ and the standard deviation is $\sigma$, the values within 1 standard deviation of the mean are in the interval $[\mu-\sigma,\mu + \sigma]$.

Step2: Set up equations

We know that $\mu = 7.5$, and the interval is from 6 to 9. Let $\mu-\sigma=6$ and $\mu+\sigma = 9$. Substituting $\mu = 7.5$ into $\mu-\sigma=6$, we get $7.5-\sigma=6$, which can be rewritten as $\sigma=7.5 - 6$. Or substituting $\mu = 7.5$ into $\mu+\sigma=9$, we get $7.5+\sigma=9$, which can be rewritten as $\sigma=9 - 7.5$.

Step3: Calculate the standard deviation

$\sigma=9 - 7.5=1.5$ or $\sigma=7.5 - 6 = 1.5$.

Answer:

1. 5