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Q.

The median wages for the following frequency distribution will be ____.


Class

Frequency

60.5-70.5

5

70.5-80.5

15

80.5-90.5

20

90.5-100.5

30

100.5-110.5

20

110.5-120.5

8


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Detailed Solution

The median wages for the following frequency distribution will be 93.5.

Class

Frequency

60.5-70.5

5

70.5-80.5

15

80.5-90.5

20

90.5-100.5

30

100.5-110.5

20

110.5-120.5

8

Given,

Class

Frequency

60.5-70.5

5

70.5-80.5

15

80.5-90.5

20

90.5-100.5

30

100.5-110.5

20

110.5-120.5

8

The formula for median:
M=l+ h× N 2 cf f   , where, l=   the lower limit of the median class, N= frequency   , and cf=   cumulative frequency.
The frequency distribution table will be:

Class

Frequency

Cumulative Frequency

60.5-70.5

5

5

70.5-80.5

15

5+15=20

80.5-90.5

20

20+20=40

90.5-100.5

30

40+30=70

100.5-110.5

20

70+20=90

110.5-120.5

8

90+8=98

  N=98 N 2 =49  
The cumulative frequency just greater than 49 is 70 and the corresponding class is 90.5100.5  .
Therefore, the median class is 90.5100.5  .
l=90.5,h=10,f=30,cf=40   and N 2 =49  
Therefore, the median is,
=90.5+ 10× 4940 30 =90.5+3 =93.5  
Hence, the median wages is 93.5.
 
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