mean, median and mode

In golf, the number of shots taken by an opponent who is out of sight is equal to the square root of the sum of the number of curses heard plus the number of swishes.

~Michael Green, The Art of Coarse Golf, 1975.

Although the quote above uses a made-up mathematical equation, the game of golf can help to explain the often-misused terms of mean, median and mode.

Let’s say you golfed nine holes. Each number below represents the number of swings it took you to sink the ball in the hole. If you’re lucky and you have some golf skills, your score is the following:

8, 4, 10, 4, 4, 5, 4, 5, 6

You go back into the clubhouse and are quite pleased with your score. You run into your friend and he says that his mean score was 6, his median was 7 and his mode was 6. So what does that mean (no pun intended)? Did you score better than your friend? Well, let’s find out.

Let’s define the term “mean” as it’s the most common term of the three and probably the easiest to explain. Basically, the mean – which is also called the average – is the sum of all numbers divided by the number of values in the list. In your golf score, you would add up all of the numbers (which equals to 50) then divide it by 9 (the number of values) and you get 5.5.

Now, let’s examine median. Basically, the median is the number that separates the higher half of a sample from the lower half. To find the median, arrange the list from lowest value to highest value and pick the middle one. Using the golf scores, here is the list from lowest to highest. The bolded 5 is the median:
4, 4, 4, 4, 5, 5, 6, 8, 10

When to use mean or median

Sometimes, you need to decide if calculating the mean or median is most appropriate for what you would like determine. Hospital length of stay can be an example of data that may be skewed if the wrong term is chosen (that is, when most of the data values fall to the left or right of the mean). Most people stay in a hospital for a few days. However, some patients have hospital stays for months on end. In this example, you would likely report the median length of hospital stay, which separates the higher half from the lower half. In general, however, most people report the mean unless you have a good reason for not doing so, such as to avoid skewing the data like in the hospital example above.

While not used as frequently as mean or median, mode does have a place in certain situations. Mode is the value that occurs most frequently in a set. If you look at your golf scores, 4 is the one that’s most common so, for that set, 4 is the mode. Although mode may not frequently be used in statistics, mode is more often used when describing non-numerical things. For example, if you’d like to know the most popular newborn boy name in Ontario for 2008, you may go to the Government of Ontario’s website and find out that Jacob was the most popular.

You can remember mode the following way: MOde is the value that is in the set MOst often.

So getting back to our golf scores example, it looks like that you likely shot a better golf score than your friend given that you had a better mean, median and mode.

Comparing the terms

Type

Description

Example

Result

Mean

Total sum divided by
number of values

(8+4+10+4+4+5+4+5+6)/9

5.5

Median

Middle value that separates
higher half from lower half

4, 4, 4, 4, 5, 5, 6, 8, 10

5

Mode

Most frequent number

4, 4, 4, 4, 5, 5, 6, 8, 10

4

 

Source: At Work, Issue 61, Summer 2010: Institute for Work & Health, Toronto

 
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