Question

The median of the following data is 28. Find the values of x
and y, if the total frequency is 50.
Marks No. of students
0-7 3
7-14 x
14-21 7
21-28 11
28-35 y
35-42 16
42-49 9

Answer 1

Dear Student,

$$\begin{gathered} N=\sum f_i \\ \Rightarrow N=3+x+7+11+y+16+9 \\ \Rightarrow N=x+y+46 \\ \sin ceN=totalfrequency=50 \\ \Rightarrow 50=x+y+46 \\ \Rightarrow \boxed{x+y=4}--\left(1\right) \\ Henceitliesinclassinterval28-35 \\ l=28,h=35-28=7,f=y,cf=cumulativefrequencytilll=28 \\ hencecf=3+x+7+11=21+x \\ andN=50 \\ NowapplymedianformulaMedian=l+\frac{{\displaystyle \frac{N}{2}}-cf}{f}\times h \\ \Rightarrow 28=28+\frac{25-\left(21+x\right)}{Y}\times 7 \\ \Rightarrow 28-28=\frac{4-x}{y}\times 7 \\ \Rightarrow 0=\frac{4-x}{y}\times 7 \\ \Rightarrow 4-x=0 \\ \Rightarrow \boxed{x=4} \\ Now\sin cex+y=4fromequation1 \\ 4+y=4 \\ \Rightarrow \boxed{y=0} \end{gathered}$$

Regards,