Question

Empirical relationship between the three measures of central tendency is
a. 2 Mean = 3 Median – Mode
b. 2 Mode = 3 Median - Mean
c. Mode = 2 Mean – 3 Median
d. 3 Median = 2 Mode + Mean

Answer 1

Hint: The relationship between mean, median and mode is known as the empirical relationship. We will take help of a defined relation, that is, Mean – Mode = 3 (Mean - Median). We will solve this relationship and select the most appropriate answer from the options.

Complete step-by-step solution -
It is given in the question that we have to find the empirical relationship between the three measures of central tendency. We know that empirical relationship is the relationship between mean, median and mode. We also know that the relationship between the three central tendencies is given as,
Mean – Mode = 3 (Mean - Median)
If we solve the known relationship between the mean, median and mode, we get,
Mean – Mode = 3 Mean – 3 Median
On transposing Mean from the LHS to the RHS, we get,
– Mode = 3 Mean – Mean – 3 Median
– Mode = 2 Mean – 3 Median
On transposing -3 Median from RHS to the LHS, we get,
3 Median – Mode = 2 Mean
It can be also written as,
2 Mean = 3 Median – Mode
Now, on comparing our result with the options given, we get to know that option (a) matches our result.
Thus, the empirical relationship between the three measures of central tendency is 2 Mean = 3 Median – Mode.
Hence, option (a) is the correct answer.

Note: The possible mistake that the students can make in this question is by writing the wrong relation between the mean, median and the mode and solving it further and getting the wrong answer. Some students may write the relation as Mean – Median = 3 (Mean - Mode), but this is wrong. Therefore, the students must remember the correct relation, that is Mean – Mode = 3 (Mean - Median) in order to solve this question.