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 (where most data falls within 1 standard deviation of the mean), if the mean is $\mu$ and the standard deviation is $\sigma$, the data within 1 standard deviation of the mean is in the interval $[\mu-\sigma,\mu + \sigma]$.

Step2: Set up equations

We know that $\mu = 7.5$, $\mu-\sigma=6$ and $\mu+\sigma = 9$. Let's use the first equation $\mu-\sigma=6$. Substitute $\mu = 7.5$ into it: $7.5-\sigma=6$.

Step3: Solve for $\sigma$

Rearrange the equation $7.5-\sigma=6$ to get $\sigma=7.5 - 6=1.5$. We can also check with the second equation $\mu+\sigma = 9$. Substitute $\mu = 7.5$ into it: $7.5+\sigma=9$, then $\sigma=9 - 7.5 = 1.5$.

Answer:

1.5