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in Statistics by (31.2k points)
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If the difference of mode and median of a data is 24, then the difference of medina and mean is 

A. 12 

B. 24 

C.

D. 36

1 Answer

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by (30.8k points)
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Best answer

Difference of mode and median, mode - median = 24 …[1] 

We know that empirical relation between mean, median and mode is 

Mode = 3 Median - 2 Mean 

⇒ 3 Mode - 2 Mode = 3 Median - 2 Mean 

⇒ 3 Mode - 3 Median = 2 Mode - 2 Mean 

⇒ 3(Mode - Median) = 2(Mode - Mean) 

From [1] we have 

3(24) = 2(Mode - Mean) 

⇒ Mode - Mean = 36 …[2] 

on substracting [1] from [2] 

Mode - Mean - (Mode - Median) = 36 - 24 

Mode - Mean - Mode + Median = 8 

Median - Mode = 8 

Hence, 

difference between median and mode is 8.

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