Question

in a certain distribution mean and median were 9.5 and 10 find the mode using empirical relationship

Answer 1

emperical formulae is 3median=mode+2mean

as per formulae 3(10)=mode+2(9.5)

30=mode+19

30-19=mode,  i.e mode=11

Answer 2

The mode of the distribution = 11

Given :

In a certain distribution mean and median were 9.5 and 10

To find :

The mode of the distribution

Concept :

The empirical relationship connecting three measures of central tendency is given by

3 × Median = 2 × Mean + Mode

Solution :

Step 1 of 2 :

Write down median and mode

Here it is given that in a certain distribution mean and median were 9.5 and 10

Median = 10

Mean = 9.5

Step 2 of 2 :

Calculate mode of the distribution

3 × Median = 2 × Mean + Mode

⇒ ( 3 × 10 ) = ( 2 × 9.5 ) + Mode

⇒ 30 = 19 + Mode

⇒ Mode = 30 - 19

⇒ Mode = 11

Hence mode of the distribution = 11

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