Question

question. for the following set of data, find the population standard deviation, to the nearest thousandth. 101, 79, 117, 99, 96, 112, 87, 75. open statistics calculator. copy values for calculator. watch video. show examples

Explanation:

Step1: Calculate the mean

The data set is \(101,79,117,99,96,112,87,75\). 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

The population 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

The population standard deviation \(\sigma=\sqrt{192.6875}\approx13.8812\approx13.881\) (rounded to the nearest thousandth)

Answer:

\(13.881\)