Math Is Fun Forum

paulb203

Member

Registered: 2023-02-24

Posts: 136

Are Cumulative Frequency graphs misleading?

I've been looking at cumulative frequency on Maths Genie.
The first value on the tables given have all been greater than x, e.g, greater than zero, or greater than 30 etc, so far.
But those first values are plotted on the graph, for example, on zero, or on 30, etc.
So the table of values tell us the first value is greater than x; but the graph seems to tell us the first value is equal to or greater than x.

Here's a link if anyone is interested; https://www.mathsgenie.co.uk/cumulative.html

Bob

Administrator

Registered: 2010-06-20

Posts: 10,181

Re: Are Cumulative Frequency graphs misleading?

hi paulb203

CFGs are an example of a statistic: a 'thing' you can get by doing some calculations on the raw data.  If you knew the actual heights of every plant, you could produce a step graph.  I'll illustrate by making up some heights.

Let's say the first 9 were 31, 33, 34, 34, 36, 37, 38, 38, 40.

You could start with a point at (30, 0) meaning no plants at 30 (or lower). Then a point at (31,1) meaning one plant at 31 or lower. Then (33, 2) meaning 2 plants at 33 or lower. And so on up to (40,9).

Then you could join them with a series of straight lines looking a bit like a staircase.

But we cannot do that because we don't know the individual heights. The only points we can be confident about are (30,0) and  (40,9). So the CFG is a compromise, intended to show something about how many plants there are at each height. You can estimate the median, for example, by looking for a point on the curve at (median, 21.5).

If you had another set of data for plants that had been growing in a new fertiliser you could compare the graphs to learn something about whether the new fertiliser helps growth. A fertiliser graph that starts rising more slowly and zooms up quickly at the end would suggest you get better growth from the fertiliser.  If the graph rises slowly at first, then zooms up quickly in the middle, then slows up as  the graph reaches 40, you could conclude that the fertiliser gives plants of more consistent height.

The point (30,0) means there are no plants with heights equal to or lower than 30. Note that the table shows 30 < h ≤ 40.  It means heights above 30 up to and including 40.

Does that help?

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

paulb203

Member

Registered: 2023-02-24

Posts: 136

Re: Are Cumulative Frequency graphs misleading?

It does help, Bob, as ever.
Thanks.