If station gets 0 calls one day and 1 call the next, what percentage of an increase mathematically

Factual Questions
1

Last year, I was listening to a radio station and the presenter said “Yesterday we got no calls to the show and today we got one call. That’s a 100% increase” and I thought “Huh that’s not right” Of course if they had one call one day and two calls the next that would be a 100% increase but is there a mathematical so answer to what increase it is it you have no calls one day and two calls the next. The problem is 100% of 0 is still 0

And 1000 x 0 is still 0

So is there an answer to what increase it is

2

Depending on how pedantic you want to get, mathematically, the increase can’t technically be expressed as a percentage. A percentage increase generally implies you begin with something. It’s a division by zero problem.

Slightly less pedantically, we can say there’s an infinitely large percentage increase. Some purists may clutch their pearls but saying it that way does express the gist in a way that generally won’t be misunderstood.

Definitely not a 100% increase, though.

3

GA is right

Note that if they got one call yesterday, and zero calls today, that would be a 100 percent decrease. Sometimes math is weird.

4

Or yesterday they received 0% of the calls they received today. In both cases it only tells you there were 0 calls yesterday and doesn’t clue you into how many you received today.

5

If I were hosting a radio show, I wouldn’t be saying on the air that no one called yesterday and only one person called today.

6

This is the only right answer, and it’s not pedantic at all. It requires dividing by zero, and you just can’t. It’s undefined.

7

I disagree with all the previous answers.

The key to dealing with percentages is to clarify percent of what? What is the base?. In most cases, where you have X in the past and Y in the present, we assume X is the base. Other times, it is stated more explicitly, such as “25% of high school dropouts…” indicates that the base is “high school dropouts”. But even then, it’s still a bit vague, because you haven’t specified if you mean all the high school dropouts that ever dropped out, or all the high school dropouts from last year, or from three years ago because that’s the most recent year for which data is available, or maybe you mean a projection for how many people will drop out this year, based on previous trends.

Granted, it makes no sense for your base to be zero, and you could not specify any percent of zero. The real question for debate here is what is the base of the percent. To answer that, we would need to talk to the person who said it, to ask for clarification.

This is why people who tell their coach “Giving 110% is impossible” are wrong. The question is 110% of what? If you assume that the base is the maximum amount that you are capable of giving, then yes, giving 110% would be impossible. But if your base is the standard amount expected by other people in similar situations, asking for 110% makes perfect sense.

In many situations, comparing X and Y, you don’t know which one should be the base, so you don’t use either of them. You pick a point in between (typically the arithmetic mean or the geometric mean) and express the difference from that central point. We used to do this in Physics all the time. You take two measurements, say 4.3 cm and 4.6 cm. You can’t really say one of them is wrong and the other is right. You can’t really say that one of them is the original and the other is a copy. They both came from the same experiment. You want to compare how close they are. You use 4.45 cm as your base and you take (4.6-4.3)/4.45=.06741573 and you say the difference between the two measurements is 6.74% .

Applying this same logic to 0 calls on Monday and 1 call on Tuesday, we can use 0.5 as our base and get (1-0)/0.5 = 200%.
Or, if last year we got 250 calls on 250 days, exactly 1 call per day, we can say the difference between 0 and 1 is 100% of last year’s average.

8

It makes me wonder about the topic of the show. I start to suspect it’s about math, with a really incompetent host. :wink:

9

With reference to sbunny8’s comments, I would like to recommend Darrell Huff’s timeless and easy-reading book, How to Lie With Statistics. Depending on what you want to prove, choosing your base may make all the difference. Also choosing your method of average, learning which figures to include and which to exclude, and how to change the subject to prove your point. It’s all in there.

10

I occasionally would threaten my math teachers that I was going to divide by zero, just to scare them–but I never had the guts to go through with it.

11

Yes, properly determining your base is critical. But your examples simply don’t work.

Giving 110% has one and only one meaning: a superlative effort. It’s not math, strictly speaking, but an idiom. The idiom depends on 100% being a maximum. Any other interpretation turns the phrase into gibberish.

Again, no one ever would use this interpretation. The question was quite properly about using 0 as a base when calculating increases. The answer to that question is “undefined.” No other answer is acceptable.

And I agree that Huff’s book is a classic.

12

I would say that they’re sampling insufficiently to make the statement they’re making. If their call volume is sufficiently low that it sometimes can be zero for an entire day, then they ought to be looking at a larger scale, like calls per week.

13

I run into this a lot with test equipment specifications. Usually, for say, a voltmeter, they may list the specification as 1% of reading. Well, obviously if the reading is being displayed as all zeros, the accuracy would be 1% of 0 or just ‘0’ meaning a perfect measurement which doesn’t exist in reality.

So any manufacturer worth a crap always specifies the 0 in absolute units rather than a ratio.

14

Just be careful of extrapolation in this situation.

15

percentage literally means “per 100”. It’s just a common reference that everybody sort-of understands. basically, it means ‘if you’d started with 100, and experienced the same rate of change, how much would it change’. In this case, we’re asking “if each person added one more, how many people would be added if there were 100 people?”. And the answer to that is simply 100.

Though, it’s looking like this might be one of those seemingly simple questions which actually divides the population, so this may be more appropriate for IMHO, or great debates.

16

In my experience, as a statistician and market researcher, an awful lot of people have a very imperfect understanding of how percentages, and percentage changes, work. I see the terminology misused, and calculations done incorrectly, all the time, and the sort of erroneous statement that the radio announcer made is pretty common.

17

It’s quite dangerous. Nobody has ever done it and lived to tell about it.

18

In the OP it is clearly stated that the percentage is for an increase from 0. The base is unequivocally 0. Everything else that follows in your post is a non sequitur.

This “logic” makes no sense. The question was not “How much higher is today’s call volume than the average of the two days?” The question was “How much higher is today’s call volume than yesterday’s?”

This is not a valid description of how to calculate a percentage. A percentage is the numerator of a fraction expressed with a denominator of 100. The phrase “if each person added one more” has no relation to the issue stated in the OP. Your description means, “If the number of people doubled from some positive number to twice that number.”

Fifth-grade arithmetic is not subject to opinion or debate.

19

Tell that to NASA. “Main engines at 108 percent, attitude nominal.”

Or The Engineering Digest, Volume 3, page 642.
“At 110% of normal voltage, the per cent. of resistance to that at normal is 99.81 with a carbon lamp, 102.5 with a tantalum lamp, and 104 with a tungsten lamp.”

Or the Russians in The Hunt for Red October.
“Captain, Engineer reports 105% on the reactor possible… but not recommended.”

Or Economist Stephen Shmanske, who wrote a paper in the Journal of Quantitative Analysis in Sports titled “Dynamic Effort, Sustainability, Myopia, and 110% Effort”, where he defines 100% as the level of effort that can be consistently sustained, and points out 110% can be done for short periods of time, it just can’t be sustained consistently.

Or the Toyota corporation in 2011.
“Automotive News reported that Toyota will run its North American plants at 110% of their capacity later this month.”

Or Jack Lemmon in The China Syndrome.
“Wait a minute. We’re at the top of the scale!”
“I got a technician in the diesel engine room. He’s got it rigged to go to 110.”

20

That’s where you lost me.

#1 You’re assuming that the OP in this thread has accurately relayed to us what was actually said on the radio.

#2 You’re assuming that what was actually said on the radio wasn’t a simple case of saying the wrong words and accidentally saying something other than what you meant to say.

I think Nikolai Lobachevsky, Kurt Gödel, and others, might disagree with you on that.