Question

if arithmetic mean of a seties is 45 and median is 40 then calculate the value of mode of that series
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Answer 1

If the Arithmetic mean of a series is 45 and the median is 40, then calculate the value of the mode of that series.

Step-by-step explanation:

• According to Karl Pearson's empirical relationship,

• To find the mean, median, and mode, the formula is

                  Mean - Mode = 3(Mean - Median)

Given, Mean = 45

           Median = 40

Substituting the values,

     ⇒ 45 - Mode = 3(45 - 40)

          45 - Mode = 3(5)

          45 - Mode = 15

           Mode = 45 -15

           Mode = 30

Therefore, the mode of the series is 30.

Answer 2

$\sf { \underline{SOLUTION}}$

GIVEN

• Arithmetic mean of a series is 45

• Median of the series is 40

TO DETERMINE

The value of mode of that series

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,

Mode = 3 × Median - 2 × Mean

EVALUATION

Here it is given that

Arithmetic mean of a series is 45 and Median is 40

∴ Mode

= 3 × Median - 2 × Mean

= ( 3× 40 ) - ( 2× 45 )

= 120 - 90

= 30

FINAL ANSWER

The value of mode of that series = 30

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