Median: Meaning, Definition, Nature, Properties, Merits & Demerits | Statistics

In this article, we will discuss the Meaning, Definition, Properties, Nature or characteristics, Properties, Merits & Demerits of Median (Measures of Central Tendency – Statistics.

Meaning of Median (Measures of Central Tendency)- Statistics

Meaning Definition of Median (Measures of Central Tendency)- Statistics

The median is a centrally located value that splits the distribution into two equal portions, one containing all values more than or equal to the median and the other containing all values less than or equal to it. The median is the ” middle ” element when the data set is organized in order of magnitude. As the median is established by the position of several values, it is unaffected if the size of the greatest value increases. The data or observations might be arranged in either ascending or descending order. In Statistics, the Median is denoted by M.

Definition of Median

Meaning Definition of Median

According to Yule and Kendall, “The median may be defined as the middlemost value of the variable when items are arranged in order of magnitude or as the value such that greater and smaller values occur with equal frequency.”

Meaning, Definition, Properties, Nature or characteristics, Properties, Merits & Demerits of Median (Measures of Central Tendency – Statistics.

Nature or Characteristics of Median

Nature or Characteristics of Median

The median is a statistical measure that represents the middle value of a dataset when it is ordered from least to greatest. Here are some key characteristics and properties of the median:

1. Middle Position: The median is the middle value in a dataset when it is arranged in ascending or descending order. It is not affected by extreme values (outliers) and provides a robust measure of central tendency.
2. Applicable to Ordered Data: Unlike the mean (average), which requires numerical values, the median can be determined for both numerical and ordinal data. It is particularly useful when dealing with ordinal data or skewed distributions.
3. Calculation: To find the median, you arrange the data in order and identify the middle value. If the dataset has an odd number of observations, the median is the middle value. If the dataset has an even number of observations, the median is the average of the two middle values.
4. Robust to Outliers: The median is not sensitive to extreme values or outliers in the dataset. This makes it a more robust measure of central tendency than the mean in situations where extreme values might distort the average.
5. Not Affected by Magnitude: Unlike the mean, which takes into account the magnitude of values, the median only considers the order. This makes it suitable for datasets with values that do not have a clear numerical interpretation.
6. Balancing Point: In a sorted dataset, the median divides the data into two halves. Half of the values are below the median, and half are above it. This provides a sense of balance in the distribution.
7. Appropriate for Skewed Distributions: The median is often preferred over the mean when dealing with skewed distributions. In cases where the data is not symmetrically distributed, the median gives a better representation of the center.
8. Useful in Describing Distributions: The median, along with other measures like the mean and mode, helps describe the central tendency of a dataset. It provides insight into where the “typical” or “central” value lies.

Properties of Median

Properties of Median

1. The sum of deviations of the items from the median (ignoring signs) is the minimum. For example, the median of series, 2, 4, 6, 9, 10 is 6. Now, the deviations from 6 after ignoring signs are 4, 2, 0, 3, 4. The total of these deviations is 13. This total is minimum from the total obtained from deviations taken from any other number. If the deviations are taken from 4, the deviations after ignoring the signs will be 2, 0, 2, 5, 6 and the total of these deviations is 15. Therefore, it can be said that the median is centrally located.

2. The median is not influenced by the extreme values as it is a positional average. 

Merits of Median

Merits of Median

It is one of the easiest and most widely used measures of Central Tendency.  Some of the merits of the Median are as follows:

1. Simple: It is one of the simplest measures of central tendency. It is quite easy to compute and simple to understand. It can be easily calculated through inspection in the case of some statistical series. 

2. Unaffected by Extreme Values: The extreme values do not affect the median of a series. For example, a median of 20, 25, 30, 35, and 120 is 30; however, its mean is 46. With this, we can see that the median is not affected by the extreme value; i.e., 120, and is thus a better average.

3. Graphical Representation: The Median can be presented graphically through ogive curves, which makes the data more presentable and understandable.

4. Appropriate for Qualitative Data: When dealing with qualitative data, the optimum average to utilize is the median. For example, measuring honesty quantitatively is not possible. However, one can easily locate an individual with average honesty through an array of a group of persons arranged in ascending or descending order of honesty.

5. Helpful in case of Incomplete or Typical Data: The median is even used in case of incomplete data as the median can be calculated even if one knows the number of items and middle items/items of a series. The median is frequently used to express a typical observation. It is influenced mostly by the number of observations rather than their magnitude.

6. Ideal Average: The median has a definite and certain value, which means that it is defined rigidly.

Demerits of Median

Demerits of Median

The demerits of Median are as follows: 

1. Arrangement of Data: The given data must be arranged in ascending or descending order to compute the Median, which can be a time-consuming task if the number of items is large.

2. Lack of Representative Character: The median does not represent a measure of such a series in which the values are widely apart.

3. Unpredictable: When the number of items is minimal, the median is unpredictable, which does not depict the true picture of the data.

4. Affected by Fluctuations: The sampling fluctuations have a significant impact on the median. It means that if the class intervals of a series are not uniform, then the median value becomes inappropriate.

5. Lack of further Algebraic Treatment: Median cannot be further algebraically treated. For example, just like in the case of the mean, it is not possible to determine the combined median of two or more groups.

6. Not based on all Observations: As the median is a positional average, it is not based on each item of a distribution. For example, the median of 10, 20, 30, 40, and 50 is 30. Now, if we replace the values 10 and 20 with 80 and 90, and replace the values 40 and 50 with 15 and 22 respectively, then it will not have any impact on the median value of the series.

7. Unrealistic assumptions in the case of Grouped Distribution: The assumption while determining the median in the case of grouped distribution is that the median class of the series is uniformly distributed, which in reality rarely happens.

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That’s all about the Meaning, Definition, Properties, Nature or characteristics, Properties, Merits & Demerits of Median (Measures of Central Tendency – Statistics.