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.
Explanation:
Consider the five data items as, 1, 2, 3, 5, 9.
Then,
[tex]\begin{gathered} \operatorname{mean}=\frac{1+2+3+5+9}{5} \\ =\frac{20}{5} \\ =4 \end{gathered}[/tex]Also,
[tex]\operatorname{median}=3\text{ (}\because\text{ n=5 is odd)}[/tex]Hence, it is proved.
Therefore, the standard deviation is,
[tex]\begin{gathered} \text{ Standard deviation}=\sqrt[]{(\frac{\sum ^{}_{}x^2}{n})-(\frac{\sum ^{}_{}x}{n})^2} \\ =\sqrt[]{(\frac{1^2+2^2+3^2+5^2+9^2}{n})-(4)^2} \\ =\sqrt[]{\frac{1+4+9+25+81}{5}-16} \\ =\sqrt[]{\frac{120}{5}-16}_{} \\ =\sqrt[]{24-16} \\ =\sqrt[]{8} \\ =2\sqrt[]{2} \end{gathered}[/tex]Hence, the standard deviation is
[tex]2\sqrt[]{2}[/tex]
