Mean, Median and Mode

Consuunt

It is simple, quick, and it seems that you’ve done more than you’ve actually done .

Nevertheless, means are not always the best option for developing your analysis.

Sometimes, Medians or Modes are much better options .

Mean

We all know what an average is:

However, when should you use averages in your Analysis?

When to use a Mean

Example of When to use a Mean

Imagine you own a retail shop .

One day, you decide to make some business forecast.

Since you have different prices for the same product sold (depending on the discount applied to the customer, the season, the supplier’s price, etc) you decide to use average prices in your calculations.

Moreover, since you calculated it by dividing your real Revenues by the real amount of products sold, the sum of all averages will be the exact Income you had:

Hence, the variable you’ll use (average prices of products sold) will give you much more accurate results than if you used the most common price of each product sold.

In this example you can easily appreciate when averages may be very useful:

But what is that we said about “numbers to be similar”?

You’ll understand it better once we’ve explained the Median :

Median

Averages are so popular that nobody cares about Medians .

However, Medians are much more useful than averages in lots of different situations.

First of all, what is a Median?

Example of Median

Let’s take this series:

If you want to know which its Median is, first of all, you should sort it :

Since this series is formed by 11 numbers, the median would be the sixth one: 5 .

What would be the average value of that series?

Compare its Median ; 5 with its Mean ; 13.9 .

What is going on? Well, that “100” is very “distorting” .

In this simple example, you can easily appreciate how much more representative the Median would be if you were developing a statistical analysis.

When to use the Median

Example of When to use the Median

Imagine that you have an e-commerce Site .

In order to do this, you have asked your clients for their personal financial situation.

You find out that:

You decide to calculate the average income of your Clients and… Surprise!

The average Income of your Clients is 10 million dollars per month!

Finally, you decide to use your customers’ Median Income in order to have a more representative analysis.

This example shows us something very important:

Analysis must be representative.

Otherwise, if you handle numbers that are far away from reality, you’ll fail miserably .

Mode

This is the easiest concept to understand.

What is the Mode?

Example of Mode

If you had the series:

1, 4, 6, 8, 2, 3, 4, 5, 10, 5, 2, 5.

Its Mode is: 5.

We all tend to use Modes in our day a day.

In each decision we take, in every conclusion we obtain… We use the “most common result” as the more likely to take place.

When to use the Mode

Example of When to use the Mode

Imagine that you own a Handmade Jewelry on-line business .

You are planning to launch a new product, but you are not sure whether it should be a necklace or a bracelet .

After a Market study, you conclude that:

You then decide to launch a new necklace .

Without even thinking about it, you developed a Mode analysis.

The answer could have never been an Average .

Since you wanted to focus on one Particular Product; a Sub-Group, you developed a Mode Analysis .

Summarizing

When should you use Averages?

When should you use Medians?

When should you use Modes?