Lessons · Teaching · averages, spread, and reading the graph they give you
Averages, spread, and the graph they give you
You need the mean, median, mode and range, you need to know which one answers a given question, and you need to read bar charts, line graphs, pie charts and scatterplots. A scatterplot question usually asks about the direction and strength of a relationship rather than about a number.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
In beta. This lesson was written for Hone and has not yet been checked by a state certification officer. Practice material, not professional advice. What that means.
What it is for
You will read data about children for the rest of your career, and the question 'which average should we quote' is one you will be in the room for. It is also the most misused piece of mathematics in public life, which makes it worth knowing properly rather than approximately.
How to think about it
Order the numbers before doing anything, because the median needs it and the range is easier from it. Pick the average by asking what the question wants: the mean for a fair share, the median when a few extreme values would drag the mean, the mode for the most common category.
Worked example
Salaries 20, 22, 23, 25, 150: the mean is 48 and the median is 2320 + 22 + 23 + 25 + 150 = 240 and 240 / 5 = 48. The median describes this group and the mean does not.
Range is largest minus smallest: 150 - 20 = 130One number, and it tells you how spread out the set is, not where its middle is.
A scatterplot sloping up from left to right shows a positive relationshipTighter points mean a stronger one. Neither says anything about cause.
A pie chart shows shares of one whole, so it cannot compare two different totalsTwo pie charts of different-sized groups look comparable and are not.
Your turn
Name the average to quote when a few extreme values would distort it.
Use the when a few extreme values would drag the mean
Solve one, graded on the server
The trap
Reading a correlation as a cause. Two things rising together is what a scatterplot can show; why they rise together is not in the picture, and the option that supplies a reason is usually the wrong one.