Question

The relation between mean, median and mode is
A. $ Mode = 3(Median) - 2(Mean) $
B. $ Mode = 2(Median) - 3(Mean) $
C. $ Mode = 3(Mean) - 2(Median) $
D. $ Mode = 2(Mean) - 3(Median) $

Answer 1

Hint: The terms mean, median and modes are used often in statistics to define different parameters of a given data set. The term mean refers to the average values of the data given in the data set, it means that what is the average data in a set can be written by,
 $ M = \dfrac{{sum{\text{ }}of{\text{ }}observations}}{{No.{\text{ }}of{\text{ }}observations}} $
The term median is the measure of what the member who is supposedly in the middle has. When the values in a list are arranged in an increasing order the median gives the value of the member in the middle.
The mode is the value of the highest value member in the dataset.

Complete step-by-step answer:
A formula was given by Karl Pearson which is an empirical formula, the formula is given as,
 $ Mean - Median = \dfrac{1}{3}(Mean - Mode) $
We will now solve using this formula to get the formula to fit into one of the options which are given in the question. The above equation on rearrangement gives,
 $ 3(Mean - Median) = Mean - Mode $
Solving further we get,
 $ 3Mean - 3Median = Mean - Mode $
 $ Mode = Mean - 3Mean + 3Median $
 $ Mode = 3Median - 2Mean $
Upon comparing with the options given in the question we can conclude that option (A) is the correct option for this question. The above relation is therefore the relation between mean, median, mode.
So, the correct answer is “Option A”.

Note: An important word of caution here is that this formula derived from Karl Pearson’s formula is an empirical formula rather than a theoretical one. What we mean by that rather than deriving from a well established formula this formula is derived solely from observations of loads and loads of data and is not exactly accurate but accurate enough to give comparable results.