Averages
Key points
Average = total ÷ how many
If the test scores are 60, 70, 80, 90 and 100, the total is 400, and 400 ÷ 5 = 80. The average answers one question: if you flattened out the bumps so everyone had the same, what would each one be?
Total 400 ÷ 5 people = an average of 80 points. The extra from the high scores is shared out to the low ones.
Picture it as levelling out
Line up some glasses of water and pour between them until every glass is filled to the same height. That height is the average. This is also why there is always someone above the average and someone below it — unless everyone was equal to start with.
One extreme value drags it away
Five people are carrying ¥100, ¥200, ¥300, ¥400 and ¥10,000. The average is ¥2,200 — but four of the five have ¥400 or less. That average does not describe this group at all. A single very large value pulls the average towards itself.
Four of the five have 400 yen or less. The average on its own hides what is really going on.
Look at the middle value too
When that happens, put the numbers in order from smallest to largest and take the one in the middle — the median. In the example above it is ¥300, which is much closer to a typical person in the group. Whenever the news reports an average income, get into the habit of asking what the median was.
Check yourself 5questions
Tap an option to check
Q1 What is the average of 60, 70, 80, 90 and 100?
Q2 Which rule gives you the average?
Q3 Four people have an average of 75 points. What is their total?
Q4 ¥100, ¥200, ¥300, ¥400, ¥10,000. The average is ¥2,200. What is wrong with using it?
Q5 What is the median (the middle value) of that data?
Jobs that use this
Every job uses this. The ones below are just where it shows up most.
Sports analyst$80k
Looks not just at a player's average score but at how much it swings from game to game. The job is spotting the player who is far more consistent than another with exactly the same average.
Maths used: AveragesMediansSpread
Quality control engineer$65k
Records the average weight of the products every day, along with how much the weights vary. Even when the average is right on target, an unusually wide spread is a sign that a machine may be going wrong.
Maths used: AveragesStandard deviationGraphs
Economics reporter / economist$85k
When reporting average income, whether the median is printed alongside it completely changes the impression readers get. Choosing which number to lead with is partly an ethical decision.
Maths used: AveragesMediansStatistics
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