Mean, Median and Mode

Image courtesy of Wikipedia

People love to calculate means.

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.

We all know what an average is:

• The sum of all numbers divided by the amount of numbers.

However, when should you use averages in your Analysis?

Whenever:

• The sum of all numbers is a quantity you need to be accurate
• The numbers studied don’t differ too much.

Imagine you own a retail shop.

• You sell different products at different prices.

One day, you decide to make some business forecast.

• You may have read Consuunt’s “Forecast Methods” page.

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.

• The (Number of products sold) * (Most Common Price) is Not equal to Total Revenues.

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

• When you are studying a whole that is composed of different parts.

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

• That Means are interesting for Series with “Similar Numbers”.

You’ll understand it better once we’ve explained the 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?

• A median is the middle number in a sorted list of numbers.

Example of Median

Let’s take this series:

• 100, 1, 2, 5, 6, 3, 5, 6, 5, 3, 5.

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

• 1, 2, 3, 3, 5, 5, 5, 5, 6, 6, 100.

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

• If there were 2 different numbers in the middle (in an even numbers series) the Median would be the average of both numbers.

What would be the average value of that series?

• 13.9.

Compare its Median; 5 with its Mean; 13.9.

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

• Now you probably understand what we said, that “averages are interesting when the numbers studied don’t differ too much”.

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

Whenever:

• You don’t need the overall sum to be precise.
• You have distorting numbers.
• The importance is in the fidelity with respect to all the Factors.

Imagine that you have an e-commerce Site.

• You are interested in offering the product that best suits them.

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

You find out that:

• 98% of your customers have a monthly wage between $1.000 and $3.000.
• Among the remaining 2% of your customers, you find Bill Gates.

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 .

This is the easiest concept to understand.

What is the Mode?

• The Mode is the most common value present in a series of numbers.

That is all.

Example of Mode

If you had the series:

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

You would have:

• 1: Once.
• 2: Twice.
• 3: Once.
• 4: Twice:
• 5: Three times.
• 6: Once.
• 8: Once.
• 10: Once.

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.

Whenever:

• You want to focus on Discrete Factors (Counted in whole numbers).
• Rather than a Global Representative Study you want to Focus on Sub-Groups.

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:

• 60% of people buying handmade jewelry buy necklaces.
• 20% buy bracelets.
• The rest of the people, buy different options.

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.

• You can’t develop a half-necklace half-bracelet.

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

When should you use Averages?

When:

• The sum of all numbers is a quantity you need to be accurate
• The numbers studied don’t differ too much.

When should you use Medians?

When:

• You don’t need the overall sum to be precise.
• You have distorting numbers.
• The importance is in the fidelity with respect to all the Factors.

When should you use Modes?

When:

• You want to focus on Discrete Factors (Counted in whole numbers).
• Rather than a Global Representative Study you want to Focus on Sub-Groups.