[Commerce Class Notes] on Measures of Central Tendency – Median Pdf for Exam

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 the 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.

The 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

 

The Data above has to be First Arranged as per their Magnitude (Lowest to Highest)

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 the 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!

The Data is Arranged as per Magnitude (Lowest to Highest)

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 this data is 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 the median is accurate over the 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 of. 

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 a 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 a few of the merits and demerits of measures of central tendency for the 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 programs. We, at , 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 app and start learning today!

Learning the Median

Median can be understood as when in a sorted list of numbers, the median is the value that is present in the middle. To get the median value in a set of data, the data has to be sorted in the value order ranging from highest to lowest or lowest to highest. The median can also be used to estimate an average or mean, but it should not be taken as the actual mean.

• If the amount of numbers is odd, then the median value is the number that is in the middle, with the same number of values above and below it.

• If the list comprises an even number of values, then we identify the middle pair and add them together, then it can be divided by the value two to return the median value.

When there are outliers present in the series that could somewhere affect the average of the numbers, sometimes the median is used instead of using the mean. Outliers or exceptions have less impact on the sequence median rather than on the mean.