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Question

If the median of a distribution given below is 28.5 then, find the value of x & y.

Class IntervalFrequency
0-105
10-20x
20-3020
30-4015
40-50y
50-605
Total60

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Solution

Step 1: Create a cumulative frequency table

Class IntervalFrequencyCumulative Frequency
0-1055
10-20x5+x
20-302025+x
30-401540+x
40-50y40+x+y
50-60545+x+y
Total60

Step 2: Find the value of x

Median = 28.5

n=60

Median lies in a class interval 20-30.

Cumulative frequency Cf=25+x

Lowerlimitl=20Higherlimitr=30Classsizeh=10Frequency=20

That is

28.5=20+30-25+x20×10[Median=l+n2-Cff×h]28.5=20+5+x228.5=40+5+x228.5×2=45+x57-45=x12=x

Step 3: Find the value of y

The sum of cumulative frequency is 45+x+y, we can write that

45+x+y=60y=60-45-xy=60-45-12y=3

Hence, the value of x and y is 12,3.


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