Question

Find the standard deviation for the group of data items ( to the nearest hundredth) 3, 7, 6, 5,4

Answer 1

Given;

`3,7,6,5,4`

STEP 1:

We need to find the mean of the data above

`\begin{gathered} \text{Mean} \\ \bar{x}=(3+7+6+5+4)/(5)=(25)/(5)=5 \end{gathered}`

STEP 2: We need to get the sum of the square of the difference of each data from the mean.

`\begin{gathered} \Sigma(x-\bar{x})^2=(3-5)^2+(7-5)^2+(6-5)^2+(5-5)^2+(4-5)^2 \\ \Sigma(x-\bar{x})^2=(-2)^2+(2)^2+(1)^2+(0)^2+(-1)^2 \\ \Sigma(x-\bar{x})^2=10 \end{gathered}`

STEP 3: We can find the standard deviation of the data using the formula below;

`\begin{gathered} \text{standard deviation }\sigma=\sqrt[]{\frac{\Sigma(x-\bar{x})^2}{n}} \\ \text{Where n is the number of data = 5} \\ \sigma=\sqrt[]{(10)/(5)} \\ \sigma=\sqrt[]{2} \\ \sigma=1.41 \end{gathered}`

Hence, the standard deviation for the group of data to the nearest hundredth is 1.41