Question

The following data has been arranged in ascending order:
24, 27, 28, 31, 34, x, 37, 40, 42, 45
a) If the median of the data is 35, find x.
b) Find Mean of the above data

Answer 1

Dear Student,

$$\begin{gathered} 24,27,28,31,34,x,37,40,42,45 \\ \left(a\right)Median=35 \\ No.ofobservations,n=10 \\ Mean(inthecaseofevenobservations)=\frac{({\displaystyle \frac{n}{2}}{)}^{th}term+({\displaystyle \frac{n}{2}}+1{)}^{th}term}{2} \\ \to 35=\frac{({\displaystyle \frac{10}{2}}{)}^{th}term+({\displaystyle \frac{10}{2}}+1{)}^{th}term}{2} \\ \to 35=\frac{({\displaystyle 5}{)}^{th}term+({\displaystyle 5}+1{)}^{th}term}{2} \\ \to 35=\frac{({\displaystyle 5}{)}^{th}term+(6{)}^{th}term}{2} \\ \to 35=\frac{34+x}{2} \\ \to 35\times 2=34+x \\ \to 70=34+x \\ \to x=70-34 \\ \to \mathit{x}\mathbf{}\mathbf{=}\mathbf{}\mathbf{36} \\ \left(b\right)Mean=\frac{Sumofallobservations}{Numberofobservations}=\frac{24+27+28+31+34+36+37+40+42+45}{10}=\frac{344}{10}=34.4 \end{gathered}$$

Regards