Question

If the median of the distribution given below is 28.5, then find the value of x and y.

$\begin{array}{cc}\text{Class interval}& \text{Frequency}\\ 0-10& 5\\ 10-20& x\\ 20-30& 20\\ 30-40& 15\\ 40-50& y\\ 50-60& 5\\ Total& 60\end{array}$

• A. x = 6, y = 7
• B. x = 6, y = 5
• C. x = 8, y = 7
• D. x = 4, y = 4

Answer 1

The correct option is C x = 8, y = 7

In this formula of median

Median $=l+\left[\frac{\frac{n}{2}-c.f}{f}\right]\times h$

l = lower limit of the median lass

n = number of observations

c.f = cumulative frequency of the class preceding the median class

f = frequency of the median class

h = class size or width of the median class

n= 60 and hence $\frac{n}{2}=30$
Median class is 20-30 with cumulative
frequency = 25 + $x$
lower limit of median class = 20, cf = 5 + $x$, f = 20 and h = 10
Median $=l+\left[\frac{\frac{n}{2}-cf}{f}\right]\times h$
$\Rightarrow 28.5=20+\left[\frac{30-5-x}{20}\right]\times 10$
$\Rightarrow \frac{25-x}{2}=8.5$
$\Rightarrow 25-x=17$
$\Rightarrow x=25-17=8$
Now from cumulative frequency, we can find the value of x+y as follows
$60=5+20+15+5+x+y$
or $45+x+y=60$
or $x+y=60-45=15$
Hence, $y=15-x=15-8=7$
$\therefore x=8\text{and}y=7$