#### The table below shows the salaries of 280 persons. Salary(in thousand (Rs)) Number of persons 5-10 10-15 15-20 20-25 25-30 30-35 35-40 40-45 45-50 49 133 63 15 6 7 4 2 1 Calculate the median and mode of the data.

Solution.

 Salary fi cf 5-10 49 49 10-15 133 49+133=182 15-20 63 182+63=245 20-25 15 245+15 = 260 25-30 6 260+6 = 266 30-35 7 266+7 = 273 35-40 4 273+4 = 277 40-45 2 277+2 = 279 45-50 1 279+1 = 280

$n= 280,\frac{n}{2}= \frac{280}{2}= 140$
f1 = 49, fm= 133, f2= 63, cf = 49, f = 133
l = 10, h = 5
median = $\iota +\frac{\left ( \frac{n}{2}-cf \right )}{f}\times h$
=$10+\frac{\left ( 140-49 \right )}{133}\times 5$
=$10+\frac{91\times 5}{133}$
=$10+\frac{455}{133}= 10+3\cdot 421$
$= 13\cdot 421$

In thousands = 13.421 × 1000 = 13421 Rs.
Mode = $\iota +\left [ \frac{f_{m}-f_{i}}{2f_{m}-f_{i}-f_{2}} \right ]\times h$

=$10+\left [ \frac{133-49}{2\times 133-49-63} \right ]\times 5$

=$10+\frac{84\times 5}{266-112}=10+\frac{84\times 5}{154}$
=10 + 2.727
=12.727
In thousands = 12.727 × 1000 = 12727 Rs.