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The following table gives the daily income of 50 workers of a factory:

Daily income (in Rs.)
100-120
120-140
140-160
160-180
180-200
No. of workers
12
14
8
6
10

The mean, mode and median of the above data will be

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Mean=143.6, Median=148.6, Mode=128.6

Mean=153.6, Median=138.6, Mode=128.6

Mean=143.6, Median=138.6, Mode=128.6

Mean=143.6, Median=138.6, Mode=138.6

answer is C.

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Detailed Solution

We have been given the data of the daily income of 50 workers of a factory:

Daily income (in Rs.)	100-120	120-140	140-160	160-180	180-200
No. of workers	12	14	8	6	10

The frequency distribution table will be:

Class	Frequency, fi	Mid-value, xi	Cumulative frequency	fixi
100-120	12	110	12	1320
120-140	14	130	12+14=26	1820
140-160	8	140	26+8=34	1120
160-180	6	170	34+6=40	1020
180-200	10	190	40+10=50	1900
	Σfi=50			Σ fixi =7180

Formula used for mean:

M e a n = ∑ f i x i ∑ f i M e a n = 718050 M e a n = 143.6

Formula used for median:

M e d i a n = l + h × N 2 − c f f

,
where,

l

=lower limit of the median class,

h

=size of the median class,

f

= frequency of the median class,

N

= sum of frequencies and

c f

=cumulative frequency of the class just preceding the median class.
Here,

N 2 = 502 = 25

The cumulative frequency just greater than 25 is 26 and the corresponding class is

120 − 140

.
Therefore, the median class is

120 − 140

∴ l = 120, h = 20, f = 14, N = 50 and c f = 12

Calculating the median, we get,

Median = 120 + 20 × 502 − 12 14 Median = 120 + 20 × 25 − 12 14 Median = 120 + 20 × 1314 M e d i a n = 120 + 20 × 0.928 M e d i a n = 120 + 18.6 M e d i a n = 138.6

Formula used for mode:

M o d e = 3 M e d i a n − 2 M e a n M o d e = 3 × 138.6 − 2 × 143.6 M o d e = 128.6

The value of mean is 143.6, median is 138.6 and mode is 128.6.
Thus, the correct option is 3.

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