Question

A sample data set has a mean of 61.1 and a standard deviation of 7.8. Find the minimum and maximum “usual” values of the data set.

45.5 and 76.7


53.3 and 68.9


51.3 and 70.9


37.7 and 84.5

Answer 1

Solution: We are given:

`Mean =61.1, Standard-deviation=7.8`

From the empirical rule of the normal distribution, we know that usual values of the data fall within 2 standard deviation from the mean.

Therefore, the minimum usual value is:

`Mean-2 * Standard-deviation`

`61.1-2 * 7.8`

`61.1-15.6`

`45.5`

The maximum usual value is:

`Mean+2 * Standard-deviation`

`61.1+2 * 7.8`

`61.1+15.6`

`76.7`

Therefore, the minimum and maximum “usual” values of the data set are:

45.5 and 76.7