Question

in the data set below, what is the standard deviation?
6 1 5 3 7 2
if the answer is a decimal, round it to the nearest tenth.
standard deviation ($\sigma$):

Explanation:

Step1: Calculate the mean

The mean \(\bar{x}=\frac{6 + 1+5 + 3+7 + 2}{6}=\frac{24}{6}=4\)

Step2: Calculate the squared differences from the mean

\((6 - 4)^2=4\), \((1 - 4)^2 = 9\), \((5 - 4)^2=1\), \((3 - 4)^2 = 1\), \((7 - 4)^2=9\), \((2 - 4)^2=4\)

Step3: Calculate the variance

The variance \(\sigma^{2}=\frac{4 + 9+1 + 1+9 + 4}{6}=\frac{28}{6}\approx4.67\)

Step4: Calculate the standard deviation

The standard deviation \(\sigma=\sqrt{\frac{28}{6}}\approx2.2\)

Answer:

\(2.2\)