I am trying to figure out how to make a correct statement with two values:

X = 59.8% Y = 26.7%

Is this correct?

X has 44.6% more apples than Y

If I wanted to use the word "margin" what does that imply?

Can I say

X has more apples than Y by a margin of 44.6%

Also, is there a cheat sheet for a non-stats person that you can point to? I tried googling but I'm not getting the words right. Thanks!

  • $\begingroup$ Both statements are mathematically incorrect and evidently ambiguous. Either one could be interpreted as meaning $X=(100 + 44.6)/100\times Y.$ Why don't you simply state the truth, such as "$X-Y$ is $33.1\%$"? $\endgroup$
    – whuber
    Apr 24, 2018 at 14:58
  • $\begingroup$ How did you calculate your X and Y in the first place ? Do they represent the proportion of apples in two baskets ? $\endgroup$
    – AshOfFire
    Apr 24, 2018 at 14:59
  • $\begingroup$ There was one basket of apples shared between 5 people. I am supposed to compare the apples for person X and Y above. But it has to be in sentence format, not calculation. Like as though it was a feature story in the news. Apologies as I am not a stats person! $\endgroup$
    – tiffylou
    Apr 24, 2018 at 15:04

3 Answers 3


In your specific case, as mentioned by whuber, both statements are incorrect.

First let me explain how they are incorrect using your example with simple figures.

  • The basket contained 100 apples to be shared between 5 people
  • X took 60% of the basket (= 60 apples)
  • Y took 27% of the basket (= 27 apples)
  • The remainder (13 apples) was split between the remaining folks

In this case, the first sentence

X has Z% more apples than Y

Means that X has Z more apples than Y (33) relatively to the number of apples possessed by Y (27). What you are looking for is a representation of the exceeding number of apples in terms of percentage.

Hence, Z should be calculated this way. $$ Z = 100*\frac{(X-Y)}{Y} = 100*\frac{33}{27} \sim 122\% $$

Because $33 = 27*122\%$

Now for the second sentence

X has more apples than Y by a margin of Z%

Margin is inappropriate in this sentence. Leaving aside that it is quite a "business-oriented" term (e.g. gross margin), margin represents an idea of proportion, so once again, with a division operated somewhere. While it could represent the calculation in the first sentence, I would strongly recommend you to avoid using this term.

So what is the appropriate wording ?

I frankly don't know how did you get the 44.6%. $X - Y = 33.1\%$, so at most, you can say.

The difference between the share of X and Y represents 33.1% of the total share/basket.

  • $\begingroup$ Playing around with the numbers, I found 26.7/59.8 = .446488, so presumably this is where the OP got 44.6% $\endgroup$ Apr 24, 2018 at 15:49

(1) X is 33.1 percentage points larger than Y.

(2) If you take this difference and divide it by X, you get 33.1/26.7 = 1.2397, so X is 124% more than Y.

(3) If you divide X by Y, you get 2.2397, so X is 224% of Y.

(4) Note that the number I got in (3) is 100% more than (2). This is because X is equal to Y plus the difference between X and Y. Since Y is equal to 100% of Y, we add 100% when going from "X is [percentage] larger than Y" to "X is [percentage] of Y.

(5) A lot of people in this sort of situation will say "X is 224% more than Y", but that is incorrect.

(6) If you divide Y by X, you get 44.6%. You seem to think that the correct statement of this is "X is 44.6% more than Y". But the actual correct statement is "Y is 44.6% of X".

(7) If X were 40%, then dividing Y by X would get 66.75%. It doesn't make sense that making X smaller increases the percentage by which X is larger than Y.


I have this problem all the time with clients/colleagues! The real answer is whatever works to make sure that it is understood. Possibly the easiest solution to that is to show your working.

I would go with "33.1 percentage points larger."
but I might say, for greater clarity:
"33.1 percentage points (that is 59.8%-26.7%) larger."

I do have one client who simply refuses to think that way. So for him, I would say
"124% larger - that is (59.8%/26.7%)."
or "larger by a factor of 124% - that is (59.8%/26.7%)." (this is close to the OP's idea of a margin)
This sounds clumsy, but is the equivalent of "twice as big" in the simple case of 40% vs 20%, say.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.