Question

the average january surface water temperatures (°c) of lake michigan from 2000 to 2009 were 5.07, 3.57, 5.32, 3.19, 3.49, 4.25, 4.76, 5.19, 3.94, and 4.34. the data set has the following statistics:

• $overline{x}=4.312$
• $sigma^{2}=0.577$

what is the standard deviation? round to the nearest thousandth.

0.333
0.760
2.077
18.593

Explanation:

Step1: Recall the formula for standard deviation

The standard deviation \(\sigma\) is the square root of the variance \(\sigma^{2}\). So, \(\sigma=\sqrt{\sigma^{2}}\).

Step2: Substitute the given variance value

Given \(\sigma^{2} = 0.577\), then \(\sigma=\sqrt{0.577}\).
Using a calculator, \(\sqrt{0.577}\approx0.760\) (rounded to the nearest thousandth).

Answer:

0.760