The concept of average is a very useful one. Those who understand it can make sense of the world. Those who don’t can be easily mislead.
What an average number means
Say you are told that an NBA shooting guard has an average of 20 points per game for the 6 games he has played this season. This means that the total scored by this player is the same as points. In other words, the total for the 6 games is the same as it would have been, had he scored 20 points in each of the games.
Friends sharing chocolates
Let’s illustrate it with a simple example: Five friends have met up to do some chocolate tasting. They each brought a different number of chocolates: Jim: 4, Sandra: 6, Nancy: 5 John: 1, and Jackson: 4.
To find out how many they brought, on average, we need to put all the chocolates together and then share them equally among the 5 friends.
Step 1: Putting all the chocolates together, we will have a plate with 20 chocolates on it.
Step 2: Sharing 20 chocolates equally among 5 friends results in each friend having 4 chocolates to taste. Sharing 20 chocolates equally among 5 people is achieved by the operation
Using the idea of an average to plan ahead
Back to our NBA shooting guard. Let’s call him Jeff. Jeff has 2 more matches to play and wants to lift his average to 22 points per match. This means that Jeff’s total, at the end of 8 matches, should be the same as though he had scored 22 points per match. In Figure 2 below, we can see what Jeff needs to do to lift his average from 20 to 22. The numbers in red are the additional points that he needs to score in the remaining two matches. If we add them up, we can see that Jeff will need to score points.
It would not matter if the 56 points in two matches were scored as 28 and 28, 50 and 6, or 30 and 26 points.
Using averages to better understand the world
According to the World Bank[1], In 2024, India’s Gross Domestic Product (GDP) was around 3.9 trillion US dollars. In the same year, Australia’s GDP was around 1.75 trillion dollars.
GDP is a measure of the economic activity in one year. The higher the GDP of a country in a particular year, the more economic activity there was in that year. This means that more money changed hands in India than in Australia.
Can we conclude from that fact that most Indians are wealthier than most Australians? Not necessarily. In 2024, the Indian population was more than 52000 times the Australian population, which must be taken into account in our analysis: A small amount of money in the hands of each of 1.44 billion people can add up to a very large sum indeed!
To find an “average”, or a number that represents the wealth of the average person in each country, we must divide the GDP figure by the size of the population. Doing this yields the GDP per capita or GDP for each person. In 2024, India’s GDP per capita was, roughly, $2,700 while Australia’s was close to $65,000!
The problem with average
Using the average figure for anything, be it chocolates eaten by a group of friends or the wealth of the typical citizen of a country, hides the variation between people. Take this example: Two students want to buy lunch from the school canteen. Mia checks her bank account and finds that she has no money. Johanna sees $200 in her account. The average amount of money in each account is $100. What good is that for Mia? She still cannot buy any food. This is why statisticians use average together with other measures that give them an idea of the variation between people.
Did you know that I kicked hundreds of AFL goals?
The legendary Tony Lockett is the record holder for the most goals kicked in the Australian Football League. He kicked 1,360 goals in his 281-game career. If he and I were in the same room, I could claim that, between us, we have each kicked 680 goals, on average!
I would love for you to leave a comment with an extravagant claim about yourself, made with the use of an average!
[1] World Bank. (2024). GDP (current US$) [Data set]. World Bank Open Data. https://data.worldbank.org/indicator/NY.GDP.MKTP.CD
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