Question

mean shoe size of the students in a math class is. 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 property of standard - deviation

In a normal - like distribution, most data (about 68%) falls within 1 standard deviation of the mean. If the range within 1 standard deviation of the mean is from 6 to 9, we can find the standard deviation using the formula for the range within 1 standard deviation of the mean. Let the mean be $\mu$, and the standard deviation be $\sigma$. The lower bound is $\mu-\sigma$ and the upper bound is $\mu + \sigma$. The range is $(\mu+\sigma)-(\mu - \sigma)=2\sigma$.

Step2: Calculate the range

The range of the data within 1 standard deviation is $9 - 6=3$.

Step3: Solve for the standard deviation

Since the range within 1 standard deviation is $2\sigma$ and the range is 3, we have $2\sigma=3$. Solving for $\sigma$, we get $\sigma=\frac{3}{2}=1.5$.

Answer:

1.5