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The mean, median and mode of the following frequency distribution will be

Class
0-10
10-20
20-30
30-40
40-50
60-70
300-350
Frequency
5
10
18
30
20
12
5

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Mean=35.6, Median=35.67, Mode=35.81

Mean=34.6, Median=35.67, Mode=35.81

Mean=35.6, Median=35.67, Mode=36.81

Mean=35.6, Median=36.67, Mode=35.81

answer is A.

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Detailed Solution

Given:

Class	0-10	10-20	20-30	30-40	40-50	60-70	300-350
Frequency	5	10	18	30	20	12	5

The frequency distribution table will be:

Class	Frequency, $f_{i}$	Mid-value, $x_{i}$	Cumulative frequency	$f_{i} x_{i}$
0-10	5	5	5	25
10-20	10	15	5+10=15	150
20-30	18	25	15+18=33	450
30-40	30	35	33+30=63	1050
40-50	20	45	63+20=83	900
50-60	12	55	83+12=95	660
60-70	5	65	95+5=100	325
	Σ $f_{i}$ =100			Σ $f_{i} x_{i}$ =3560

Formula used for mean:

M e a n = ∑ f i x i ∑ f i

Substituting the values:

M e a n = ∑ f i x i ∑ f i M e a n = 3560100 M e a n = 35.6

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.
We know that,

N 2 = 1002 = 50

, the cumulative frequency just greater than 50 is 63 and the corresponding class is

30 − 40

.
Therefore, the median class is

30 − 40

∴ l = 30, h = 10, f = 30, N = 100 and c f = 33

Calculating the median, we get

Median = l + h × N 2 − c f f Median = 30 + 10 × 1002 − 33 30 Median = 30 + 10 × 50 − 33 30 Median = 30 + 10 × 1730 M e d i a n = 30 + 10 × 0.567 M e d i a n = 30 + 5.67 M e d i a n = 35.67

Formula used for mode:

M o d e = 3 M e d i a n − 2 M e a n

Substituting values, we get

M o d e = 3 M e d i a n − 2 M e a n M o d e = 3 × 35.67 − 2 × 35.6 M o d e = 35.81

The value of mean is 35.6, median is 35.67 and mode is 35.81.
Thus, the correct option is option 1.

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