Question

Empirical relationship between the three measures of central tendency.
4 Median = Mode + 2 Mean
Or, Mode = 3 Median – 2 Mean

Answer 1

Hint: The empirical formula is calculated using a relation that difference of mean and mode is three times the difference of mean and median which is represented as : Mean – Mode = 3 (Mean - Median) which on simplification we get,
Mode = 3 Median – 2 Mode

Complete step-by-step answer:
In the question we are given two empirical formulas of measures of central tendency in terms of mean, median and mode we have to tell which of them is true.
At first we will tell briefly about each of the terms in the formula.
The word mean is more commonly known as average. So mean can be calculated by adding all the data values together and then dividing by total number of values just like how average is calculated.
The term median is the midpoint of the distribution of values on any cases, with an actual number of cases above and below the median. The median is calculated by listing the data values in ascending order, then finding the middle value in the list.
The mode is the value that occurs most often in the distribution. It is calculated by counting how many times each value occurs. The value that occurs with the highest frequency in the mode.
In x statistics, there is a relationship between the mean median and mode that is empirically based. Observations of countless data sets have shown that most of the time the difference between the mean and mode is three times the difference between the mean and the median. The relationship in equation form is:
Mean – Mode = 3 (Mean – Median), which on simplification we get,
Mean – Mode = 3 Mean – 3 Median
Hence on rearranging and simplifying we get,
Mode = 3 Median – 2 Mode
So, the equation is, Mode = 3 Median – 2 Mode.

Note: If we don’t have the details of data values but we know the values of any two of mean, median and mode then we can find the third quantity using the empirical formula which is also considered as one of the applications.