Measures of Central Tendency – Median

Measures of central tendency refer to a single value that helps to correctly describe a set of data through the identification of the central position within a said data set. There are three valid central tendency measures, namely – mean, median and mode. As per the measures of central tendency definition, these are collectively classed as summary statistics.

While mean, median and mode are all valid measures for central tendency, some of them are more appropriate and accurate than others.

Following is an elaboration on median, as one of the most significant among various measures of central tendency. 

Median – Definition and Calculation

Median is a middle score in a set of data arranged according to their magnitude. It is used to divide a collection of data into two parts, where one half includes values that are greater than or equal to the median; whereas the second half contains values that are lesser than or equal to the median value.

Median value, unlike other measures of central tendency formulas, is not influenced by skewed data or outliers.

Now, if the observations in a variable are ordered by value, then a median value is given by the value corresponding to the middle value in that said ordered list. That is, the median value corresponds to that of a cumulative percentage of 50%, and its position is given by – {(n+1)/2} Th value; where “n” is the number of values present in that dataset.

Following is an example of the calculation of median value – 

95

73

86

14

21

53

35

64

49


The data above has to be first arranged as per their magnitude (lowest to highest) – 

14

21

35

49

53

64

73

86

95


Here, the median value is 53, since it is the middle mark, and five values are lying before it and five values after it. However, this method for computing median works if there is an odd number of data present in the set. What happens if the number of data present is even?

Take a look!

95

73

86

14

21

53

28

35

64

49

 

The data is arranged as per magnitude (lowest to highest) – 

14

21

28

35

49

53

64

73

86

95

Here, we consider the fifth and sixth data from this sequence and their average is the median in this scenario. That is,

Median = (49+53)/2 = 51

Properties of Median

Median is considered among the best measures of central tendency owing to its following properties – 

  • Calculating a median does not depend on all the values of data present in a dataset.

  • It is the value given by the middle point of the data set, such that half of these data are present above it and the other half is situated below it.

  • Every array of data has a single median.

  • The value for a median remains stable in a grouping procedure.

  • Medians cannot be determined for interval, rational, and ordinal scales.

  • The measure for median is accurate over mean when the distribution of data is skewed.

  • Medians cannot be combined or weighed or in general, manipulated algebraically.

Merits and Demerits of Median

As far as merits and demerits of central tendency – median are concerned, there are several of which to take note. 

Following are a Few Merits of Median – 

  • It is easily understandable and computable.

  • It is well defined as an average.

  • It is not influenced by extreme values in a data set and is also independent of the dispersion and range of data.

  • Median can be utilised in the case of computing frequency distribution with open-ended classes.

  • It can be plotted graphically with the help of an ogive curve.

  • It can be used as a proper average for qualitative data for which items are scored, instead of being measured.

  • In a few cases, a median is a better measure of average than mean.

Following are Some of the Demerits of Median – 

  • Since the computation of a median requires data to be arranged in ascending or descending order of value, it can be time-consuming when a data volume is large.

  • It can be affected by fluctuations in sampling, more than that in the case of Arithmetic mean.

  • It only gives a positional average and does not consider the magnitude of data.

  • Since it does not consider all observations, it cannot be considered the ideal representation of the average.

  • In case of considerable variation among data, the median will not be able to represent the data efficiently.

  • Since it is a positional average, further algebraic treatment for the data is not possible. For instance, computing the combined median between two groups of data is not possible.

  • It neglects considering the extreme values.

Here are few of the merits and demerits of measures of central tendency for median. 

To learn more about median merits and demerits, alongside its integration in the calculation of central tendency, you can refer to our online learning programmes. We, at Vedantu, have also introduced online live classes, which can assist you in learning about the advantages and disadvantages of the measures of central tendency and other such topics, from experts in the field. 

So, without further ado, install the Vedantu app and start learning today!

FAQ (Frequently Asked Questions)

1. What are the Merits and Demerits of Mean, Median, Mode?

Mean is rigidly defined. However, it can become inaccurate and affected by the presence of very high or low data. Contrarily, median remains unaffected by anomalies and can be used for extreme values. It is, however, not useful for smaller data sets. Mode is the only measure of central tendency that can be used for nominal data. Nonetheless, the value of mode can be unreliable due to the presence of more than one modal value.

2. What are the Advantages of Mean, Median and Mode?

Computing arithmetic mean is simple and can be used for the interval or ordinal sets of data. Median is advantageous since it remains unaffected by skewed data and is useful for ordinal data. Finally, a mode is useful for the calculation of nominal data, and the resulting modal value is present in the given data set.

3. What is Median?

Median, given the positional value of a number, is present in the middle of a given data set. It helps to divide a data set into two equal parts, with one half giving the values greater than the median and the other half giving values lower than the median.