Question

If the mode of a distribution is 12 and the mean is 3, then the median is
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Answer 1

Given :- If the mode of a distribution is 12 and the mean is 3, then the median is ?

Solution :-

we know that, the relationship between mode , median and mean is :-

• Mean - Mode = 3 (Mean - Median)

given :-

• Mode = 12 .
• Mean = 3 .

Putting values we get,

→ 3 - 12 = 3(3 - median)

→ (-9) = 9 - 3median

→ 3median = 9 + 9

→ 3median = 18

→ median = 6 (Ans.)

Hence, the Median of the distribution will be 6.

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Answer 2

SOLUTION

GIVEN

The mode of a distribution is 12 and the mean is 3

TO DETERMINE

The median

CONCEPT TO BE IMPLEMENTED

Mean

In measure of central tendency mean is the most common measure.

For a given set of observations mean is the average value of a group of numbers.

It is obtained by adding up all the observations divide by the number of observations

Median

Median is the middle most value of a set of observations when the samples are arranged in order of magnitudes ( Either in ascending or in descending)

Mode

For a set of observations mode is defined to be the value ( or values) of the sample ( or samples) which will occur with maximum frequency.

Mean is based on all the observations and if one of the observation is changed, the mean will also change. On the other hand median and mode may remain unchanged even if a number of sample values be changed.

For symmetrical frequency distribution

Mean = Mode = Median

For asymmetrical frequency distribution

But for moderately asymmetrical distribution there is an approximate relation between them and it is given by

Mean - Mode = 3 ( Mean - Median)

That is,

$\sf{Mode + 2 \times Mean = 3 \times Median}$

EVALUATION

Here it is given that

Mode = 12 , Mean = 3

So this is an asymmetrical frequency distribution

Hence

$\sf{Mode + 2 \times Mean = 3 \times Median}$

$\sf{ \implies \:12 + (2 \times 3)= 3 \times Median}$

$\sf{ \implies \: 3 \times Median = 18}$

$\sf{ \implies \: Median = 6}$

FINAL ANSWER

Hence Median = 6

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