In the data set below, what is the standard deviation? 8251946 If the answer is a decimal, round it to the nearest tenth. standard deviation (d): (sigma ):square

## Step 1: Calculate the mean ($\mu$)<br />### Sum all the numbers and divide by the count: $\mu = \frac{8+2+5+1+9+4+6}{7} = \frac{35}{7} = 5$<br /><br />## Step 2: Calculate the squared differences from the mean<br />### Subtract the mean from each number, square the result, and sum these squared differences: $(8-5)^2 + (2-5)^2 + (5-5)^2 + (1-5)^2 + (9-5)^2 + (4-5)^2 + (6-5)^2 = 9 + 9 + 0 + 16 + 16 + 1 + 1 = 52$<br /><br />## Step 3: Calculate the variance ($\sigma^2$)<br />### Divide the sum of squared differences by the number of data points: $\sigma^2 = \frac{52}{7} \approx 7.42857$<br /><br />## Step 4: Calculate the standard deviation ($\sigma$)<br />### Take the square root of the variance: $\sigma = \sqrt{\frac{52}{7}} \approx \sqrt{7.42857} \approx 2.72554$. Rounded to the nearest tenth, $\sigma \approx 2.7$