The story of Mean:
I think you all know me :) I am introduced to you in your schools. I am just AVERAGE. Most people call me average. But I get angry when people call me average because there exist other types of averages too (median, mode, etc). People call me using μ. My formula is the sum of all values present divided by the total number of values. But,
I have a problem — 😒
I am blown away when there are outliers!! You may ask what are outliers. Well, they are the values which are very much greater than the average values present in the data. Haven’t understood? Let me explain it with an example. Let us consider marks in a class. Let’s assume the marks of students has a mean 8 GPA, but there is one TOPPER, who gets a 9.8 GPA. Now whats the mean of the class?? Is it 8 or something else? Well, we might intuitively think that the mean should be 8, but it’s not!
What’s the problem?? The problem is with TOPPER. If we add his GPA to the entire class GPA, the mean GPA will increase so much, which is obviously incorrect. So here, the TOPPER GPA is an outlier.
Let’s define it more formally — An outlier is an observation that lies an abnormal distance from other values in a random sample from a population.
Therefore, the mean is heavily affected by outliers.
I have one more problem.
I am not always present in the data.
The mean you get, may not be present in the data itself! Example, consider, 1,2,3,101,102,103. The mean is 52. But 52 is itself not a value in the data.
So what to do now? Don’t worry, Median comes into the rescue!