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:

$Mean-2 \times Standard-deviation$

$61.1-2 \times 7.8$

$61.1-15.6$

$45.5$

The maximum usual value is:

$Mean+2 \times Standard-deviation$

$61.1+2 \times 7.8$

$61.1+15.6$

$76.7$

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

45.5 and 76.7