Relation Between Mean, Median, and Mode

To grasp the meanings of mean, median, and mode and the link between them and the difference, it is necessary first to realize that they are all part of measures of central tendency. It refers to a single number that seeks to represent a feature of an entire set of data by pinpointing the set's central location. It is sometimes referred to as a measure of the central position. Measures of central tendency were commonly referred to as "averages" informally. However, we now have far more than average. The mean, median, and mode are the most frequent metrics of central tendency.

Mean: The term "mean" refers to an arithmetic mean. Other forms of 'mean,' such as geometric and harmonic mean, are outside the purview of this article. The average of a group of integers is referred to as the arithmetic mean. In simple terms, it is the summation of magnitudes of all items present in a collection to the number of items present in that particular collection. The mean definition of a particular data set is the average for a certain number of data sets determined.

Median: When a data collection is sorted in either descending or ascending order, the median is the number in the center. The median value is the number in the middle if there is a set of odd numbers and the simple average of the midway pair in the dataset if there are even numbers. Since it minimizes exceptions, the median is far more efficient than the average or mean.

Mode: The most common number in a dataset is referred to as the mode. A collection of numbers might have only one mode, several modes, or none at all. The mode of a data set is the number with the highest frequency, which is derived by counting the number of times each data value appears. The relationship between mean, mode, and median are defined by two methods. The first is the empirical relationship, and the second is the relation due to frequency distribution.

Empirical Relation between Mean, Mode, and Median

When the data is distributed as moderately skewed, the difference between the mean and the mode is equivalent to 3 multiplied by the difference between the mean and the median. This is calculated using the empirical relation.

Frequency Distribution

According to the frequency distribution, there are three relations amongst the mean, median, and mode. They are as follows:

Symmetrical Frequency Curve: If the frequency distribution is symmetric, which means that it is identical on both sides from the highest magnitude, then the mean, mode, and median are equal to each other.

Positively Skewed Curve: For a skewed frequency distribution, the relationship changes a little bit. The positively skewed curve always has the mean with a higher value, followed by the median, and the mode has the smallest value.

Negatively Skewed Curve: For a negatively skewed curve, the relationship again changes. The mean has the least value. The median has a value greater than the mean, while the mode has the highest value of all.