Question

in the data set below, what is the standard deviation?
3 7 6 4 9 5 1
if the answer is a decimal, round it to the nearest tenth.
standard deviation (σ):

Explanation:

Step1: Calculate the mean

The mean \(\bar{x}=\frac{3 + 7+6 + 4+9 + 5+1}{7}=\frac{35}{7} = 5\)

Step2: Calculate the squared differences from the mean

\((3 - 5)^2=(- 2)^2 = 4\)
\((7 - 5)^2=2^2 = 4\)
\((6 - 5)^2=1^2 = 1\)
\((4 - 5)^2=(-1)^2 = 1\)
\((9 - 5)^2=4^2 = 16\)
\((5 - 5)^2=0^2 = 0\)
\((1 - 5)^2=(-4)^2 = 16\)

Step3: Calculate the variance

The variance \(\sigma^{2}=\frac{4 + 4+1 + 1+16 + 0+16}{7}=\frac{42}{7}=6\)

Step4: Calculate the standard deviation

The standard deviation \(\sigma=\sqrt{6}\approx2.4\)

Answer:

\(2.4\)