#### Size of agricultural holdings in a survey of 200 families is given in the following table: Size of agricultural holdings (in ha) Number of families 0-5 5-10 10-15 15-20 20-25 25-30 30-35 10 15 30 80 40 20 5 Compute median and mode size of the holdings

Solution.
$mode= \iota +\left [ \frac{f_{m}-f_{1}}{2f_{m}-f_{1}-f_{2}} \right ]\times h$

 Size of agricultural holdings fi cf 0-5 10 10 5-10 15 25 10-15 30 55 15-20 80 135 20-25 40 175 25-30 20 195 30-35 5 200

(i) Here n = 200

$\frac{n}{2}= \frac{200}{2}= 100$ which lies in interval  (15 – 20)

l = 15, h = 5, f = 80 and cf = 55

$median = l+\frac{\left ( \frac{n}{2}-cf \right )}{4}\times h= 15+\frac{\left ( 100-55 \right )\times 5}{80}$
=$15+\frac{45}{16}= 15+2\cdot 81= 17\cdot 81$
l = 15, fm = 80, f1 = 30, f2 = 40 and h = 5
$mode= \iota +\left [ \frac{f_{m}-f_{1}}{2f_{m}-f_{1}-f_{2}} \right ]\times h$

$= 15+\left [ \frac{80-30}{2\times 80-30-40} \right ]\times 5$
$= 15+\left [ \frac{50}{160-70} \right ]\times 5$
$= 15+\left [ \frac{50}{90} \right ]\times 5$

=$15+\frac{25}{9}$
=15 + 2.77 = 17.77