Basic Statistics: Mean, Median and Mode

Mean, median and mode are three common terms used in statistics that are used frequently to describe numerical data like housing prices, grades, car prices, etc. Knowing how they are figured and how they relate can be helpful when doing comparison shopping or figuring out your grades.

Mean or average is the sum of all items in the list divided by the total number of items in the list.

Median is literally the middle number in the list of items when the list is arranged highest to lowest.

Mode is simply the number that appears in the list the most often.

To the left is a list of numbers representing the prices of homes in the same general area. (The numbers are made up for our use.)

To find the mean or average add all the numbers and divide by 10 (the total number of items in the list).

The sum for our list is 2,066,599. Divide by 10 and the mean or average price for a home on the list is 206,659.90.

To the right are the same numbers from the list above left but in order from highest to lowest.

To find the median you use one of two methods depending on if the total number of items is odd or even. In this list, there are an even number of items.

- Find the exact middle of the list, green line.
- Average the two middle numbers (in the red circle the numbers are the one above and the one below the green line). First add the 210,000 + 189,500 = 399,500 now divide by 2 399,500 ÷ 2 = 199,750.

But, what if we have an odd number of entries in our list?

Here we have the same list of numbers but we have added 157,999 giving us eleven entries in our list. How do we find the median? Find the entry with the exact same number of entries above it and below it (blue circle).

So, what is the mode? The number that appears the most often. I n this case 250,000 which appears 3 times (purple box). You can have a list with no mode (no number appears more than once) or with multiple modes. Multiple modes will occur when you have two numbers that appear on the list the same number of times. If items 8, 9 and 10 were all 168,300 then the list would have 2 modes.

We know how to find the mean median and mode but what do they tell us?

Scenario: You are looking to buy a home in a specific neighborhood and want to spend about $200,000. Your realtor could tell you that a median priced home in the area sells for $199, 750 based on the list with 10 entries. Ok, that sounds good. Next, they tell you most homes sell for about $250,000. Oh, too high. However, the average price of a home in the area is $206,660. Ok, that could be doable. Because two of the data numbers are near your target figure there is a pretty good chance you can find a home in your range. If you were to look at the list of entries you would see that at least half are well within your budget.

Mean, median and mode are a way to look at summaries of large amounts of data, tools to help us make choices. Given a list with hundreds of entries having the mean, median and mode can give us basic information to begin making decisions about the information. In our housing scenario, we may decide to view some of the houses available in the area. They reduce mountains of information into manageable bites.