Question

18 7 19 7 25 23
send data to excel
the population variance for the e - books is.
the population standard deviation for the e - books is.

Explanation:

Step1: Calculate the mean

The data set is \(18,7,19,7,25,23\). The mean \(\mu=\frac{18 + 7+19+7+25+23}{6}=\frac{99}{6} = 16.5\)

Step2: Calculate the squared - differences

\((18 - 16.5)^2=1.5^2 = 2.25\), \((7 - 16.5)^2=(-9.5)^2 = 90.25\), \((19 - 16.5)^2=2.5^2 = 6.25\), \((7 - 16.5)^2=(-9.5)^2 = 90.25\), \((25 - 16.5)^2=8.5^2 = 72.25\), \((23 - 16.5)^2=6.5^2 = 42.25\)

Step3: Calculate the population variance

The population variance \(\sigma^{2}=\frac{2.25 + 90.25+6.25+90.25+72.25+42.25}{6}=\frac{303.5}{6}\approx50.583\)

Step4: Calculate the population standard deviation

The population standard deviation \(\sigma=\sqrt{50.583}\approx7.112\)

Answer:

The population variance for the e - books is approximately \(50.583\).
The population standard deviation for the e - books is approximately \(7.112\).