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:

x = 4.312
2 = 0.577
What is the standard deviation? Round to the nearest thousandth.

0.333
0.760
2.077
18.593

Answer 1

Answer:0.760

just right by chance

Answer 2

Answer: Second Option

`\sigma=0.760`

Explanation:

We have the average January surface water temperatures (°C) of Lake Michigan from 2000 to 2009.

5.07, 3.57, 5.32, 3.19, 3.49, 4.25, 4.76, 5.19, 3.94, 4.34

We know that the average
`{\displaystyle {\overline {x}}}` of the data is:

`{\displaystyle {\overline {x}}}=(\sum_(i=1)^(10)x_i)/(10)=4.312`

We also know that the variance
`\sigma^2` is equal to 0.577.

So by definition the standard deviation
`\sigma` is:

`\sigma=√(\sigma^2)\\\\\sigma=√(0.577)\\\\\sigma=0.760`