Question

in the data set below, what is the standard deviation?
7 9 1 9 4 6 6
if the answer is a decimal, round it to the nearest tenth.
standard deviation (σ):

Explanation:

Step1: Calculate the mean

The data set is \(7,9,1,9,4,6,6\).
The mean \(\bar{x}=\frac{7 + 9+1+9+4+6+6}{7}=\frac{42}{7} = 6\)

Step2: Calculate the squared differences

\((7 - 6)^2=1\), \((9 - 6)^2 = 9\), \((1 - 6)^2=25\), \((9 - 6)^2 = 9\), \((4 - 6)^2=4\), \((6 - 6)^2=0\), \((6 - 6)^2=0\)

Step3: Calculate the variance

The variance \(\sigma^{2}=\frac{1+9+25+9+4+0+0}{7}=\frac{48}{7}\approx6.86\)

Step4: Calculate the standard deviation

The standard deviation \(\sigma=\sqrt{\frac{48}{7}}\approx2.6\)

Answer:

\(2.6\)