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Relation between Mean, Median and Mode

Derive the fo...

Question

Derive the formula or the relationship between mean, mode,and median of a set of numbers, i.e.,
Mode=(3×median)-(2×mean)
In an asymmetrical set of numbers

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Solution

This is a formula which relates mean, median and mode of a group of observations or data values. It does not have any theoretical proof, but comes from practical observation of a group of data.

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Similar questions

Q. The empirical relation between mean, mode and median is

(a) Mode = 3 Median − 2 Mean

(b) Mode = 2 Median − 3 Mean

(c) Median = 3 Mode − 2 Mean

(d) Mean = 3 Median − 2 Mode

Q. The relationship between mean, median and mode for a moderately skewed distribution is

(a) Mode = 2 Median − 3 Mean
(b) Mode = Median − 2 Mean
(c) Mode = 2 Median − Mean
(d) Mode = 3 Median −2 Mean

The relation between mean,mode and median is

(a) $m o d e = (3 \times m e a n) - (2 \times m e d i a n)$

(b) $m o d e = (3 \times m e d i a n) - (2 \times m e a n)$

(c) $m e d i a n = (3 \times m e a n) - (2 \times m o d e)$

(d) $m e a n = (3 \times m e d i a n) - (2 \times m o d e)$

Q. Assertion :If mean & median of an asymmetrical distribution are

58

61

respectively, then Mode

= 67

. Reason: For an asymmetrical distribution Mode

= 3

- 2

Q. For the set of numbers 2, 2, 4, 5 and 12, which of the following statements is true?

(a) Mean = Median

(b) Mean > Mode

(c) Mean > Mode

(d) Mode = Median

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