M&M&M : Mean ~ Median ~ Mode : Uncovered

August 05, 2015 Wajdi Ben Saad

Is it just me , or people are still confusing the 3 M's?

I've made a general observation about the common mistakes some folks make when talking about statistical concepts., that they can not differentiate between the mean, mode and median of a particular data variable.

For statisticians and domain experts, this might seem like a "stupid" topic to talk about, since statistics are actually a very deep field, and those 3 points are just small dots in an ocean of concepts and knowledge .

But it is very important for those who work with numbers, to really get the idea behind some of the basic concepts they see or use everyday, because as confusing as it might seem for some people, an argument where you use the "mean" as a variable to justify a decision you made will be totally wrong if what you were really referring to in your reasoning was the "Mode"

Mean:

The mean is simple the average value of the set of values you have in your hand.
Let's say you have a set of 9 values : (3,2,8,1,0,5,3,8,4). To calculate the mean value you have to sum all these values and divide them by the count of values which is in this case 9. Which gives us a mean of 3.777778.
More generally, there are many types of means. The one we just calculated is the "arithmetic mean".
For a sample of $x_1,x_2,\ldots,x_n$ numbers, it's formula is :

$\bar{x} = \frac{x_1+x_2+\cdots +x_n}{n}$

There are other types of means like the geometric mean and the harmonic mean as well. But the most commonly used is the arithmetic mean.

Median:

The median is also a simple concept to understand. For a given data sample, when you arrange it in ascending order, the median is the value that separates the upper half of the data and the lower half. In our example :
The data : (3,2,8,1,0,5,3,8,4)
The sorted data : (0,1,2,3,3,4,5,8,8)
Data count = 9 elements
The median value is = 3. It separates 4 elements on the right and 4 on the left : (0,1,2,3,3,4,5,8,8)

In the case when we don't have a single middle value, the mean is also defined as the mean of the two middle values. If we add to our data the value 9 we'll have:

The data : (3,2,8,1,0,5,9,3,8,4) The sorted data : (0,1,2,3,3,4,5,8,8,9) Data count = 10 elements The median value is = 3,5. Because: (0,1,2,3,3,4,5,8,8,9) two middle values, their mean is : (3+4)/2 =3,5

Mode:

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Aug 5, 2015