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.

Answers (1)

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.
 

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