Question

The following table shows the distribution of savings by in group individuals in thousands per annum. Find the median.

Savings (in thousands)		Number of individuals
	0-20		42
	21-30		48
	31-40		120
	41-50		84
	51-60		48
	61-70		36
	71-80		31

• A. 41000
• B. 41540
• C. 40460
• D. 50000

Answer 1

Answer: (C)

Median $=$ size of $\frac{N^{\text {th }}}{2}$ item $=$ Size of $(\frac{399}{2})^{\text {th }}$ item $=199.5^{\text {th }}$ item
Which lies in $(31-40)$ group
$\therefore$ Median class is $30.5-40.5$
Median $=l_1+\frac{\frac{N}{2}-c f_0}{f} \times(l_1-l_2)$
$=30.5+\frac{199.5-80}{120} \times 10$
$=30.5+\frac{119.5}{12}=40.46$ (in thousands)
$=40.46 \times 1000$
$=40460$