Question

What is the relation between mean, median, and mode?
(a) Mode = 3 Median + 2 Mean
(b) Mode = 3 Median – 2 Mean
(c) Mode = 2 Median – 3 Mean
(d) Mode = $${\displaystyle \frac{Median+mean}{2}}$$.

Answer 1

Hint: We know that Mode is defined as the value that appears most often in a set of data values, mean is defined as the sum of the values present in a set divided by the total number of values present in that set of values and Median is defined as the middlemost number in the sorted ascending or descending order of a set of values. We use the fact that the relation between the mean, median, and mode “Mode = Mean – 3(Mean – Median)” to proceed through the problem.

Complete step-by-step solution:
According to the problem, we need to find the relation between mean, median, and mode.
We know that the relationship between mean, median, and mode is defined as
$\Rightarrow$Mode = Mean – 3(Mean – Median).
$\Rightarrow$Mode = Mean – 3 Mean + 3 Median.
$\Rightarrow$Mode = 3 Median – 2 Mean.
We have found the relation between mean, median, and mode as Mode = 3 Median – 2 Mean.
∴ Mode = 3 Median – 2 Mean.
So, the correct option for the given problem is (b).

Note: We can also verify the obtained by taking a set of values and finding the mean, median, and mode of that set. We can see that these results can be viewed from the plots of Normal Distribution, Gamma distribution, and some other probability distributions. We should not confuse the definition of mean, median, and mode while solving the problems related to them.