Question

data set: 2, 5, 7, 8, 10, 15, 23
variance: ( s^{2}=\frac{1}{6}sum_{i = 1}^{7}(x_{i}-overline{x})^{2}=49.3 )
standard deviation: ( s=sqrt{s^{2}}=sqrt{49.3}approx7.02 )
the standard deviation is about 7.02.
in 20 words or fewer, what is the standard deviation of a data set if the variance is approximately 916.7?

Explanation:

Step1: Recall the formula

The formula for standard deviation \(s\) is \(s = \sqrt{s^{2}}\), where \(s^{2}\) is the variance.

Step2: Substitute the value

Given \(s^{2}=916.7\), then \(s=\sqrt{916.7}\).

Step3: Calculate

\(\sqrt{916.7}\approx30.28\)

Answer:

\(30.28\)