Question

question. for the following set of data, find the population standard deviation, to the nearest hundredth. 102, 138, 107, 112, 125, 91, 134, 110. answer. attempt 1 out of 2. open statistics calculator. copy values for calculator. submit answer. watch video. show examples

Explanation:

Step1: Calculate the mean

First, find the sum of the data values: $102 + 138+107 + 112+125+91+134+110=819$. There are $n = 8$ data - points. The mean $\mu=\frac{819}{8}=102.375$.

Step2: Calculate the squared - differences

For each data value $x_i$, calculate $(x_i-\mu)^2$.
$(102 - 102.375)^2=(- 0.375)^2 = 0.140625$
$(138 - 102.375)^2=(35.625)^2 = 1269.140625$
$(107 - 102.375)^2=(4.625)^2 = 21.390625$
$(112 - 102.375)^2=(9.625)^2 = 92.640625$
$(125 - 102.375)^2=(22.625)^2 = 511.890625$
$(91 - 102.375)^2=(-11.375)^2 = 129.390625$
$(134 - 102.375)^2=(31.625)^2 = 999.140625$
$(110 - 102.375)^2=(7.625)^2 = 58.140625$

Step3: Calculate the variance

The population variance $\sigma^{2}=\frac{\sum_{i = 1}^{n}(x_i-\mu)^2}{n}$.
$\sum_{i = 1}^{8}(x_i-\mu)^2=0.140625 + 1269.140625+21.390625+92.640625+511.890625+129.390625+999.140625+58.140625 = 3081.875$
$\sigma^{2}=\frac{3081.875}{8}=385.234375$

Step4: Calculate the standard deviation

The population standard deviation $\sigma=\sqrt{\sigma^{2}}$.
$\sigma=\sqrt{385.234375}\approx19.63$.

Answer:

$19.63$