For the data set: 5, 7, 9, 11, 13, the standard deviation is:

The correct answer is Option (1) → 2.83

The standard deviation measures how far the values lie from their mean: it is the square root of the average of the squared deviations from the mean, \(\displaystyle \sigma=\sqrt{\frac{\sum(x-\bar{x})^{2}}{n}}\).

• The mean: \(\displaystyle \bar{x}=\frac{5+7+9+11+13}{5}=\frac{45}{5}=9\)

• Deviations from the mean are \(-4,-2,0,2,4\), and their squares are 16, 4, 0, 4, 16

• Their sum is 40, and the variance (their average) is \(\displaystyle \frac{40}{5}=8\)

• The standard deviation is its square root: \(\sigma=\sqrt{8}=2\sqrt{2}\approx\) 2.83

Tip: 3.16 is \(\sqrt{10}\), what comes from dividing the sum of squares by \(n-1=4\) (the sample standard deviation). For a given set of data, divide by the number of values, \(n\).