question\nfor the following set of data, find the population standard deviation, to the nearest…

Answer:

14.916

Explanation:

Step1: Calculate the mean

$\bar{x}=\frac{101 + 79+117+99+96+112+87+75}{8}=\frac{766}{8}=95.75$

Step2: Calculate the squared - differences

$(101 - 95.75)^2=(5.25)^2 = 27.5625$ $(79 - 95.75)^2=(-16.75)^2 = 280.5625$ $(117 - 95.75)^2=(21.25)^2 = 451.5625$ $(99 - 95.75)^2=(3.25)^2 = 10.5625$ $(96 - 95.75)^2=(0.25)^2 = 0.0625$ $(112 - 95.75)^2=(16.25)^2 = 264.0625$ $(87 - 95.75)^2=(-8.75)^2 = 76.5625$ $(75 - 95.75)^2=(-20.75)^2 = 430.5625$

Step3: Calculate the variance

$\sigma^{2}=\frac{27.5625+280.5625+451.5625+10.5625+0.0625+264.0625+76.5625+430.5625}{8}=\frac{1541.5}{8}=192.6875$

Step4: Calculate the standard - deviation

$\sigma=\sqrt{192.6875}\approx14.916$