If the Difference of Mode and Median of a Data is 24, Then Find the Difference of Median and Mean. - Mathematics

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Answer in Brief

If the difference of mode and median of a data is 24, then find the difference of median and mean.

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Solution

Given that the difference of mode and median of a data is 24. That is,

MODE - MEDIAN = 24

⇒ MODE = MEDIAN + 24

We have to find the difference between median and mean

We know that

 MODE = 3 × MEDIAN - 2 × MEAN

⇒ MEDIAN + 24 = 3 × MEDIAN - 2 × MEAN 

⇒ 24 = 3 × MEDIAN - MEDIAN - 2 × MEAN  

⇒ 24 = 2 × MEDIAN - 2 × MEAN 

⇒ 2 × MEDIAN  - 2 × MEAN = 24 

⇒ 2( MEDIAN - MEAN ) = 24 

⇒ MEDIAN -MEAN = `24/2`

⇒ MEDIAN - MEAN = 12 

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Chapter 24: Measures of Central Tendency - Exercise 24.5 [Page 21]

APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 24 Measures of Central Tendency
Exercise 24.5 | Q 10 | Page 21

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