Why do we use averages?

Answer 1

There are three kinds of average that as useful in different ways.

The mean average effectively tells you what the value would be if every value were the same.

The median average tells you what the value in the middle is; exactly half the data is less than this value and half the data is greater than it.

The mode average tells you the value that occurs most often (the most popular value); this does not have to be numeric.

The first and last are particularly useful in business, especially retail (selling goods); For example a shoe shop would need to know how many of each size (and style) of shoe it sells to ensure it buys the right stock to sell on. However, knowing the most popular (Mode average) shoe allows it to check that it is making the right amount of profit . If the (mean) average selling price of shoes is not enough to cover its costs the shop would soon go out of business. Knowing these allows the shop owner to make decisions about which shoes to stock.

The Median average is used by Government when reporting census data as this is unaffected by extreme values and means that half the values are above average and half are below average.

When the word "Average" is unclassified (ie the type of average is not specified) most people will think of the mean average (as that is the first average that is met at school and the other two are not met until years later). However, this lack of awareness by the public can be used by unscrupulous people to "enhance" data for their own ends, especially when the Mean and Median averages are significantly different.

For example: When talking about average salaries the mean average is very likely to be much higher than the median average because the distribution of salary values is heavily skewed by the top people: Suppose a company has 50 employees (excluding the directors) who earn a mean average of 15,000 a year, and 2 directors who earn 110,000 each; including the directors pay increases the mean average to about 18,300 - sounds a good wage but most employees will be confused as they will see that their wages are less than this. The median average is not affected by large values at one end and sill remain at 15,000. Going further suppose that 20 of the employees only work part time (because it fits their life style) and each earns 10,000 a year and at most 10 of the rest of the employees earn the same amount; this makes the Mode average only 10,000. So the average salary could be 10,000, 15,000 or about 18,300 depending upon which average you use; and the choice of average would be based on the point you want to make: the directors earn ten times the average salary of 10,000 each so they can easily afford a large pay rise; the average salary is 18,300 each so a large pay rise isn't needed...

Averages also need to be used with care (especially by manufacturers). A fridge manufacturer looked at the average family size and was going to manufacture fridges for that size until one of the people deciding the fridge size noted that most of the people in the meeting either had no children or much more than the average - there were few families of the "average" family size.

Answer 2

Roughly speaking, an average gives a good idea of a general tendency.