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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 − c f 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

90.5 − 100.5

.
Therefore, the median class is

90.5 − 100.5

l = 90.5, h = 10, f = 30, c f = 40

and

N 2 = 49

Therefore, the median is,

= 90.5 + 10 × 49 − 40 30 = 90.5 + 3 = 93.5

Hence, the median wages is 93.5.

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