Check My Math Please!

March 11, 2016 8:55 AM

I need this for a work report, so I want to make sure I am doing this right. Could someone please verify or correct me, please? I have two percentages and I need to figure out what percentage of change has taken place. 64.24% has changed to 74.24% So, I think I need to do this: 74.24 - 64.24 \ 64.24 = 15.6% improvement or 74.24 - 64.24 \ 74.24 = 13.5% decrease
posted by LilithSilver to Work & Money (9 answers total)

Is 64.24% the original (first) value, that changes to 74.24%? In that case it is indeed a 15.6% INCREASE (change divided by original value), so your first option.
posted by swordfishtrombones at 9:02 AM on March 11, 2016 [1 favorite]

Think about it this way. 64.24 has increased to 74.24. You will want to end up with an increase in percentage. So the latter way you had it wouldn't work, as you're ending up with a decrease.

The first way is correct. (original number - final number)/original number.

So, (74.24 - 64.24) / 64.24 = 15.6% improvement.
posted by three easy payments and one complicated payment at 9:02 AM on March 11, 2016

Best answer: Assuming that more is good, it's an improvement and your first formula indicates how much of an improvement it is.

But, it really depends on what it is you are measuring. Let's say that it is percentage of students graduating from school. In the past it was 64.24% and now it is 74.24%, hoorah. The way this would normally be reported is NOT, the graduation rate has improved 15.6% (your formula). That's technically correct but it would be misunderstood as "the rate has gone up by 15.6%, which it has not. So the way to state this is to say, we've gone up 10% in our graduation rate, from 64.24% to 74.24%. Substitute the thing you are measuring for "graduation rate".
posted by beagle at 9:03 AM on March 11, 2016

Beagle is correct, but I didn't to complicate things. Percentages of percentages are generally not advisable, but I don't know the context.
posted by swordfishtrombones at 9:06 AM on March 11, 2016

Best answer: You are already working with percentages so it is just a straight addition or subtraction. If something has a value of 64.24% and it increases to 74.24%, it has increased by 10%. You do not divide by the starting percentage.
posted by incolorinred at 9:25 AM on March 11, 2016

Best answer: In that case, I would say "our graduation rate has gone up 10 percentage points" to make it clear what I'm talking about.
posted by zachlipton at 9:29 AM on March 11, 2016 [11 favorites]

Yeah, to keep it from being confusing I think you want to talk about either percentage points, as beagle and incolorinred have it, or else use absolute items instead of percentages in describing the change. That is, do either of these things:

• "...increased by ten percentage points, from 64.24% to 74.24%..."
• "...increased from x graduates last year to y graduates this year, a 15.6% increase..."

I would not characterize a change from 64.24% to 74.24% as a change of 15.6%, not because it is inaccurate but because it is terribly confusing.
posted by gauche at 9:37 AM on March 11, 2016 [2 favorites]

Also, it's good pointing out that if the change in percentage points is small, but the value is near 100%, it can be much more impressive sounding to report the change as a reduction in the "not" amount.

Examples:
A 97% to 99% success rate change would be a 2 percentage point increase or a 2.06% increase. Doesn't sound very impressive.

That same number could also be stated as the failure rate which would be from 3% down to 1% which is a 2 percentage point decrease (still doesn't sound very impressive) but this is also a 67% reductionin the rate of failures. Now that sounds impressive!
posted by soylent00FF00 at 9:40 AM on March 11, 2016 [3 favorites]

Response by poster: Thank you all! I think I was making it more complicated than it needed to be. I am going with the simple addition and subtraction method on the report.
posted by LilithSilver at 10:22 AM on March 11, 2016