Question

If the median of 60 observations, given below is 28.5, find the values of x and y.
Class interval 0-10 10-20 20-30 30-40 40-50 50-60
Frequency 5 x 20 15 y 5

Answer 1

45 + x + y = n

45 + x + y = 60

=> x + y = 60 - 45

x + y = 15 --------( 1 )

n = 60 => n/2 = 30,

f = 20 ,

c.f = 5 + x ,

l = ( 20 + 20 )/2 = 40/2 = 20

h = 10 ,

Median = l + [( n/2 - cf ) /f ] × h

28.5 = 20 +{ [ 30 - ( 5 + x ) ]/20 } × 10

28.5 = 20 + ( 25 - x )/2

28.5 - 20 = ( 25 - x )/2

8.5 = ( 25 - x )/2

17 = 25 - x

17 - 25 = - x

- 8 = - x

Therefore ,

x = 8 ,

Substitute x = 8 in equation ( 1 ) ,

8 + y = 15

y = 7

x = 8 , y = 7

I hope this helps you.

: )

Answer 2

$\begin{gathered}\boxed{\begin{array}{cccc}\sf Class\: Interval &\sf Frequency&\sf C.F\\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\\\sf 0 - 10 &\sf 5 &\sf 5 \\\\\sf 10 - 20 &\sf x &\sf 5+x \\\\\sf 20 - 30 &\sf 20 &\sf 25+x \\\\\sf 30 - 40 &\sf 15 &\sf 40+x \\\\\sf 40 - 50 &\sf y &\sf 40+x+y \\\\\sf 50 - 60 &\sf 5 &\sf 45 + x + y \\\\\sf Total &\sf n = 60 &\sf\end{array}}\end{gathered}$