How does one clearly express this statistical information relating to percentages?

Factual Questions
1

Say I know that Factor A has a rate of increase of 50%.

If I want to say that it has increased to a rate of increase of 75%, how do I express that in a way that won’t be misunderstood? If I say “The rate of increase has increased 50%” it could be understood to mean 75% or 100%.
If I say that the 50% rate of increase has increased by 10%, that could be understood to mean either 60% or 55%.
In other words, how do I simply and clearly distinguish between a percentage of a percentage and an absolute number of percents, especially when what I want to describe is the trend rather than particular data points in that trend?

2

Misunderstood by whom?

You could say “the rate of increase has grown an additional 25 percentage points, a 50% change in the rate” or similar, explicitly using both forms.
But it’s a complicated thing, and somebody may still boggle over it. Context counts.

3

This is a common issue with relative humidity (RH). Let’s say the RH was 20% yesterday, and today the RH is 30%. How much did it increase?

Both of these answers are correct:

  1. The RH is 50% higher today compared to yesterday.
  2. The RH is 10 percentage points higher today compared to yesterday.
    Another example: Last year, the average interest rate on 30 year mortgages was 4%. This year it is 5%. How much did it increase?

Both of these answers are correct:

  1. The average interest rate is 25% higher this year compared to last year.
  2. The average interest rate is 1 percentage point higher this year compared to last year.
4

Express it as a differential equation involving second derivatives?

That way, each reader (depending on his/her math acumen) will understand it perfectly well, or not at all. :slight_smile:

Know your audience.

5

Increased “by a factor of 50%” vs increased 50%? “an increase of 50%” would also mean the gross adding of, and not a factor of (to me at least). I would play it safe and just say “increased from 50% to… x%”. That is, if you want as much transparency as possible rather than merely decreasing the confusion quotient by 10%… to 10%… whatever.

6

In many financial numbers, they’ll use the phrasing as an increase or decrease in basis points. There are 100 basis points in each 1%. So if interest rates go from 3.5% to 4.0%, that would commonly be described as an increase of 50 basis points.

7

If you’re just looking for clarity, I don’t see how you can beat “the rate of increase has gone from 50% to 75%”. Like pancakes3 said.