Question

A data set has a mean of 50 and a standard deviation of 10. Which of the following might possibly be true?

No less than 30% of the data values are less than 30 or greater than 70.

At least 15% of the data values are less than 20 or greater than 80.

At least 89% of the data values are between 20 and 80.

No more than 50% of the data values are between 30 and 70.

Answer 1

At least 89% of the data values are between 20 and 80.

Explanation:

We use the Chebyshev's inequality to solve this problem. It states that:

A minimum of 75% of the measures lie within 2 standard deviations of the mean and a minimum of 89% of the measures lie within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 50, standard deviation = 10.

So a minimum of 75% of the measures are between 50-2*10 = 30 and 50 + 2*10 = 70 and a minimum of 89% of the measures are between 50-3*10 = 20 and 50+3*10 = 80.

So the correct answer is:

At least 89% of the data values are between 20 and 80.