Question

2. If the median and mode of the data are 52 and 52.4
respectively, then its mean is.........

Answer 1

$\sf { \underline{SOLUTION}}$

GIVEN

The median and mode of the data are 52 and 52.4 respectively

TO DETERMINE

The mean

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

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

Mean - Mode = 3 ( Mean - Median)

∴ Mode + 2 × Mean = 3 × Median

EVALUATION

Here it is given that

Median = 52

Mode = 52.4

∴ 52.4 + 2 × Mean = 3 × 52

$\implies \sf{2 \times Mean = 156 - 52.4}$

$\implies \sf{2 \times Mean = 103.6}$

$\implies \sf{ Mean = 51.8}$

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Answer 2

Answer:

Mean = 51.8

Step-by-step explanation:

Given,

         Median = 52

         Mode = 52.4

We know the relation

        Mode = 3 Median - 2 Mean

⇒ 52.4 = 3 (52) - 2 Mean

⇒ 52.4 = 156 - 2 Mean

⇒ 2 Mean = 156 - 52.4

⇒ 2 Mean = 103.6

⇒ Mean = 103.6 / 2

⇒ Mean = 51.8

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