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

Answers (1)

Answer. [17.77]

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

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