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.
(1 point)
○ 51.3 and 70.9
○ 45.5 and 76.7
○ 53.3 and 68.9
○ 37.7 and 84.5

Explanation:

Step1: Recall the formula for usual values

Usual values are within \( \mu\pm2\sigma\) where \(\mu\) is the mean and \(\sigma\) is the standard deviation.

Step2: Calculate the minimum usual value

\(\mu - 2\sigma=61.1-2\times7.8\)
\(=61.1 - 15.6\)
\(=45.5\)

Step3: Calculate the maximum usual value

\(\mu + 2\sigma=61.1+2\times7.8\)
\(=61.1+15.6\)
\(=76.7\)

Answer:

45.5 and 76.7