Question

in the data set below, what is the standard deviation?
5 9 1 7 1 2 3
if the answer is a decimal, round it to the nearest tenth.
standard deviation (σ):

Explanation:

Step1: Calculate the mean ($\mu$)

The data set is \(5,9,1,7,1,2,3\).
The mean \(\mu=\frac{5 + 9+1+7+1+2+3}{7}=\frac{28}{7} = 4\)

Step2: Calculate the squared differences \((x_i-\mu)^2\)

• For \(x_1 = 5\): \((5 - 4)^2=1\)
• For \(x_2 = 9\): \((9 - 4)^2 = 25\)
• For \(x_3 = 1\): \((1 - 4)^2=9\)
• For \(x_4 = 7\): \((7 - 4)^2 = 9\)
• For \(x_5 = 1\): \((1 - 4)^2=9\)
• For \(x_6 = 2\): \((2 - 4)^2=4\)
• For \(x_7 = 3\): \((3 - 4)^2=1\)

Step3: Calculate the variance (\(\sigma^{2}\))

\(\sigma^{2}=\frac{1+25 + 9+9+9+4+1}{7}=\frac{58}{7}\approx8.2857\)

Step4: Calculate the standard deviation (\(\sigma\))

\(\sigma=\sqrt{\frac{58}{7}}\approx2.9\)

Answer:

\(2.9\)