Question

What is the standard deviation of the number of letters received in a week?

Answer 1

First get the mean of the data set.

`\begin{gathered} \mu=\sum (x_i)/(N) \\ \text{where} \\ x_i\text{ is the elements in the data set} \\ N\text{ is the number of entries in the data set} \\ \\ \text{There are 7 entries in the data which means that} \\ \overline{}\mu=(3+7+4+4+5+8+2)/(7) \\ \overline{}\mu=(33)/(7) \\ \mu=4.71428571 \end{gathered}`

After getting the mean we can now get the standard deviation

`\begin{gathered} \sigma=\sqrt[]{(\sum (x_i-\mu)^2)/(N)} \\ \\ \text{where} \\ \mu\text{ is the mean or the average} \\ x_i\text{ are the entries} \\ N\text{ is the number of entries} \\ \\ \sigma=\sqrt[]{(\sum(x_i-\mu)^2)/(N)} \\ \sigma=\sqrt[]{((3-4.71428)^2+(7-4.71428)^2+\cdots+(2-4.71428)^2)/(7)} \\ \sigma=\sqrt[]{3.9183673469388} \\ \sigma=1.9794866372216 \end{gathered}`

Rounding off to 3 decimal places, the standard deviation is 1.979.