Question

Make up a set of five data items whose mean is 4 and whose median is 3. Show your answer is correct. Find the standard deviation of your data.

Answer 1

Given

Make up a set of five data items.

The mean of a five data items is 4.

The median is 3.

To show that the answer is correct and to find the standard deviation of your data.

Step-by-step explanation:

Consider the five data items as, 1, 2, 3, 5, 9.

Then,

Also,

Hence, it is proved.

Therefore, the standard deviation is,

`\begin{gathered} \text{ Standard deviation}=\sqrt[]{(\frac{\sum ^{}_{}x^2}{n})-(\frac{\sum ^{}_{}x}{n})^2} \\ =\sqrt[]{((1^2+2^2+3^2+5^2+9^2)/(n))-(4)^2} \\ =\sqrt[]{(1+4+9+25+81)/(5)-16} \\ =\sqrt[]{(120)/(5)-16}_{} \\ =\sqrt[]{24-16} \\ =\sqrt[]{8} \\ =2\sqrt[]{2} \end{gathered}`

Hence, the standard deviation is

`2\sqrt[]{2}`