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Question:

The table shows the salaries of 280 persons. Salary (In thousand) No. of Persons 5 60 10 63 15 15 20 65 25 15 Calculate the median salary of the data.

Solution:

Salary(In thousand) Frequency(f)Cumulative frequency(cf)
5 60 60
10 63 123
15 15 138
20 65 203
25 15 218
Total no. of persons N=60+63+15+65+15+6+7+4+2+1=280
Now, N/2 = 140
cf ≥ N/2 is 123
Median class is 10-15
f = 63
Lower limit of median class l = 10
c.f. above the median class is 60
Width of the interval h = 5
Median = l + [(N/2 - c.f)/f]h = 10 + [(140 - 60)/63]5 = 10 + (80/63)5 = 10 + 6.35 = 16.35
Hence, median = 16.35