the average january surface water temperatures (°c) of lake michigan from 2000 to 2009 were 5.07, 3.57…

Explanation:

Step1: Recall variance formula

The formula for the variance $s^{2}$ of a sample is $s^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}$, where $n$ is the number of data - points, $x_{i}$ are the individual data - points, and $\bar{x}$ is the mean. Here, $n = 10$.

Step2: Sum the squared differences

From the table, $\sum_{i=1}^{10}(x_{i}-\bar{x})^{2}=0.575 + 0.551+1.016 + 1.259+0.676+0.004+0.201+0.771+0.138+0.001=5.192$.

Step3: Calculate the variance

Using the formula $s^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}$, substitute $n = 10$ and $\sum_{i=1}^{n}(x_{i}-\bar{x})^{2}=5.192$. Then $s^{2}=\frac{5.192}{10 - 1}=\frac{5.192}{9}\approx0.577$.

Answer:

$0.577$