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?

Answer 1

The standard deviation of the shoe size data for the math class is 1.5.

Step-by-step explanation:

We are given that 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.

Let the standard deviation of the shoe size be represented by '$\sigma$' and the mean shoe size be represented by '$\mu$ = 7.5'.

Also, the sizes of the shoe be represented by '$x$'.

Now, according to the question, the first condition states that most of the shoe sizes fall within 1 standard deviation, that is;

                  $\mu - 1 \sigma < x < \mu + 1 \sigma$   -------------- [equation 1]

And the second condition states that most of the shoe sizes fall between a size 6 and a size 9, that is;

                        $6 < x<9$  ------------------- [equation 2]

Now, comparing equation 1 and equation 2 we get;

$\mu - \sigma = 6$  and  $\mu + \sigma=9$

$7.5 - \sigma = 6$  and  $7.5 + \sigma=9$     {substituting the value of $\mu$}

$\sigma = 7.5-6$  and  $\sigma=9-7.5$

So, $\sigma = 1.5$.

Hence, the standard deviation of the shoe size data for the math class is 1.5.