Given:
The sample is
[tex]4,8,14,7,0,8,2,10,3,12[/tex]Find-:
The sample mean and the median
Explanation-:
The mean formula is
[tex]\text{ Mean }=\text{ }\frac{\text{ Sum of observations}}{\text{ Total number of observations}}[/tex]So, mean is
[tex]\begin{gathered} \text{ Mean }=\frac{4+8+14+7+0+8+2+10+3+12}{10} \\ \\ \text{ Mean }=\frac{68}{10} \\ \\ \text{ Mean }=6.8 \end{gathered}[/tex]The mean is 6.8
The median is:
Total number of observation (n) = even
So, the median is
[tex]\text{ Median }=\frac{(\frac{n}{2})^{th}\text{ term}+(\frac{n}{2}+1)^{th}\text{ term}}{2}[/tex][tex]\begin{gathered} n=10 \\ \\ \frac{n}{2}\text{ term }=\frac{10}{2}=5\text{ term} \\ \\ 5\text{ terms }=0 \\ \\ (\frac{n}{2}+1)\text{ terms }=6\text{ terms} \\ \\ 6\text{ term }=8 \\ \\ \end{gathered}[/tex]The median is:
[tex]\begin{gathered} \text{ Median }=\frac{(\frac{n}{2})^{th}\text{ term }+(\frac{n}{2}+1)^{th}\text{ term}}{2} \\ \\ \text{ Median }=\frac{0+8}{2} \\ \\ \text{ Median }=\frac{8}{2} \\ \\ \text{ Median }=4 \end{gathered}[/tex]The median is 4
