How to compute the percentage of difference between two values?

Question

If there are two real values called week1val and week2val, what operation is required to calculate the percentage of difference between the two values? Does the higher of the two values need to be used for calculation, the lower of the two, or what?

For example, with these particular values:

week1val = 2.77
week2val = 2.84
diff = (week2val - week1 val) // (0.07)

...how is the percentage of difference between the two values computed? Is it like so:

pct = diff div [the larger of week1val and week2val] // In the contrived case: "0.07 div 2.84"

...or:

pct = diff div [the smaller of week1val and week2val] // In the contrived case: "0.07 div 2.77"

...or some other way???

Answer 1

You can express this different ways, but the easiest and traditional is to state by what percentage of the first value the second value differs from the first value.

so: ${week2val - week1val \over week1val}$, and then multiply by $100$ to express as a percentage.

Thus ${2.84 - 2.77 \over 2.77} 100 = 2.527 \%$. You would say, "the second week value is $2.527\%$ greater than the first week value".

Answer 2

There is no blanket rule to pick either one. It all depends on the context of the problem. If one number is your "standard", use it. If there is no particular "standard", I would suggest that you use their average:

$\displaystyle \frac{(wv_1-wv_2)}{(wv_1+wv_2)/2)}$

And David G. Stork is right too. I guess the names of the variables are not enough for me to decide which one you want to use "first".

Answer 3

It is entirely context dependent. You're choosing what you want to use as a "baseline" option.

• If you're looking at something year by year, you will often compare to the older year.
• If you're comparing a statistic and a population's mean, you'll compare to the population mean.
• If you're looking to compare two individual data points where you can't differentiate them in another way, you arbitrarily use one as the baseline and compare the other to it.

That being said, anecdotally, I'm marginally more accustomed to seeing the smaller value used as the baseline, but that may even be related to fields of study and places of employment.

Answer 4

A guideline is that the "original" value should go in the denominator.

In the case of week 1 and week 2, assuming that you are moving forward in time, week 1 value would be the natural choice for the "original" value.

However, it all depends on what you are trying to measure. Suppose the periods were year 1 and year 10, and you were trying to find out how much cheaper cars were in year 1, you would treat year 10 value as "original", i.e. the base value with which comparisons were being made.