Mean, Median and Mode Application And Example

It is very important to understand the correct usage of the measures of central tendencies or mainly the mean, median and mode. People end up using only mean or average without checking the data set properly. In this article we will see how to determine which central tendency value to consider.

To read more about measure of central tendencies please click here and here.

When to use mean, median and mode? Many people end up using only mean for their data without investigating their data. Median and Mode are also central tendencies which should be inspected before moving ahead for any further.

 Do you think that average height of any class of students represents the height of that group? Similarly, does mean of placement package of a college, the best way to judge if the students of that college had good placement?

On professional front, is average sales figure the best figure to compare it with previous values and with that of competitors? Is average income of a country, state or area truly represents the population income of that place? If someone tells that the average no of customers prefer their particular feature of the product, does it really mean that all the people buying the product prefer that particular feature?

Well Experts say NOT ALWAYS.

How? Let us see through some examples.

Is Average Height OK?

For cultural event in a school, decision was taken to distribute different works to different classes. The committee decided the decoration work will be given to class whose average height should not be less than 140 cm (4.6 ft. / 55 inch). After going through the data of average height of different classes in the school, class 4 met with these criteria. Let us investigate if this is correct decision.

Histogram Of Data Of Class 4

Download the working file from the below link

In this class 4 of 30 students, the mean height is 141.38 cm, Median of 135.80 cm and Mode of 135.67 cm. As per the criteria fixed of average height more than 140 cm, the class passes, but it is found that about 57% of the students have height less than the mean height of the class, which is 141.38 cm also less than 140 cm, the minimum criteria decided. Now it is evident that average is not always the best criteria to decide the characteristics of any group. In the above case, Median value would have been the best indicator, even better than mode.

You can see from the above that, if the distance of all the data from the mean i.e. difference between individual data both on the right hand side and left hand side of the mean, and mean of the data set is not equal, the average value does not necessarily represent the data set.

Average Placement Package of College

You have taken admission in an MBA college after looking in the highest package offered to the last batch from a particular department. Did you miss something to check out before considering the college? Just check the breakup of the package offered to the previous batch in the excel sheet. The Highest package of 10 Lakhs is insignificant here, so what about the average package? 70% of the students have received offers, which are less than the average of 4.3 Lakh per annum. Again, average package does not seem to be a good option here. The median salary of 3.9 lakh per annum will somehow justify the data set. Now think, did you do the right thing by joining the college?

Sales Comparison

Let us see if the same can be applied in a particular situation where two companies having similar product are selling and the sales for a particular month is available in the excel sheet for reference. The two companies have same value of total sales figure of the month, so can we check the average weekly sales figure? Oops, they are same. Now, when we further delve into the individual weekly sales values, we see that Company 1 leads in the first three weeks and only lags behind in the last week. Therefore, we can see that Company 2 did extremely well in the last week to equal the values and arrest the rank of Company 1.

Therefore, we can see here that it also depends on which stage’s average value you are taking into consideration for comparing.

From above two examples, you can see that in most of the real life cases, not all the data surrounding the mean is equidistant from the mean of the data set, so it becomes very critical to check whether average should be considered or any other values of central tendency should be considered.