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What are the derivations for the formula of mode and median in statistics?

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Q. 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

Q. The test marks in statistics for a class are

20, 24, 27, 38, 18, 42, 35, 21, 44, 18, 31, 36, 41, 26, 29

. The median score of the class is?

Q. The word statistics and statistical are derived from the Latin word status, means _______ state.

Q. For a frequency distribution, mean, median and mode are connected by the relation

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

Q. Calculate the mean and median for the folllowing data:

Marks	:	10	11	12	13	14	16	19	20
Number of students	:	3	5	4	5	2	3	2	1

Using empirical formula, find its mode.

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