Find the mean, median, and mode of the following frequency distribution:

Class Interval
0-10
10-20
20-30
30-40
40-50
50-60
60-70
Frequency
4
    5
7
10
12
   8
   4

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Mean = 18, Median = 78, Mode = 43.33

Mean = 48.2,Median = 52,Mode = 43.33

Mean = 37.2, Median = 39, Mode = 43.33

Mean = 42, Median = 39, Mode = 43.33

answer is C.

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Detailed Solution

We have been given the frequency distribution of the data.

Class Interval	0-10	10-20	20-30	30-40	40-50	50-60	60-70
Frequency	4	5	7	10	12	8	4

The given frequency distribution is,
Question Image

From the above table, it can observed that, A = 35,

∑ f i = 50

and

∑ f i u i = 11.

The value of mean by using the assumed mean formula,

Mean = A+ ∑ f i u i ∑ f i × C

,
where, A =assumed mean and c = size of class interval.

⇒ Mean = 35 + 115010 ⇒ Mean = 35 + 2.2 ⇒ Mean = 37.2

Hence, the mean of the given data is 37.2.
The median can be calculated using,

Median = l + n 2 − c f ∑ f i × h

where l= lower limit of median class,
h = size of the class interval,
n = total number of observations,
cf = cumulative frequency Substitute 30 for l and 50 for n and 16 for cf and 50 for

∑ f i

and 10 for h in formula.

⇒ Median = 30 + 502 − 16 10 × 10 ⇒ Median = 30 + 25 − 16 ⇒ Median = 39

Hence, the median of the given data is 39.
The Mode is given by,

Mode = l + f 1 − f 0 2 f 1 − f 0 − f 2 × h

where l= lower limit of modal class,
h = size of the class interval,
f0 = frequency of modal class,
f1 = frequency of preceding class,
f2 = frequency of succeeding class
Substitute 40 for l and 12 for

f i

and 10 for

f 0

and 8 for

f 2

and 10 for h,

⇒ Mode = 40 + 12 − 10 212 − 10 − 8 × 10 ⇒ Mode = 40 + 20 24 − 18 ⇒ Mode = 40 + 206 ⇒ Mode = 40 + 3.33 ⇒ Mode = 43.33

Hence, the mode of the given data is 43.33.
Hence, the mean, median, and mode of the distribution are 37.2, 39, and 43.33 respectively.
Therefore, the correct answer is option (3).

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