In the context of a pie chart, the percentages are absolutely meaningless. I wrote about a better visualization approach in I Keep Saying, Use Bar Charts, Not Pies.

The total is a percentage, sure, but completely meaningless.

One figure can be 193% of another. Your car example is a good one. The number of dogs in my family pets example is 120% the number of cats. Both of these make sense.

If you want to use your nickel example to say that each person has an average of 1.73 nickels, well, mathematically is makes sense, but this information is less useful than, say, the change in the number of cars on the road.

David Schwartz: The total support votes cast for the candidates of interest was 193% of the number of people casting such votes.

What does this even mean? So you want to say that the average person polled supported 1.93 of the candidates? Totally nonsensical in a pie chart, and not relevant in a rational discussion.

The approval of one candidate is not independent of approval of the others. Someone in favor of Palin is more likely to be in favor of the others than someone who disapproves of Palin. 193% is a silly number derived in a silly way by someone who doesn’t understand arithmetic, proportions, or charts.

If 60% of the people in my family has a pair of blue jeans and 80% has a pair of black jeans, do 140% of us have jeans?

The total support votes cast for the candidates of interest was 193% of the number of people casting such votes.

Or, here’s another way to do it. You get 53 people in a room. You ask then each to give you all their nickels. You get 92 nickels. The number of nickels you got can accurately be described as 173% of the number of people in the room. That doesn’t mean there are more people, just more nickels.

David Schwartz: 193% of the people who cast support votes.

What? It’s not that at all. The three candidates have support of 70, 63, and 60% of the people polled. Are you saying then that 193% of the people polled did were combined into the chart? No, there’s a lot of overlap between the 70, 63, and 60%. I’ll bet nearly everyone who supported Romney also supported Palin. When there is overlap like this, a pie chart is not confusing, it is stupid, and it is wrong.

You want to make the pie chart even better? Include Newt Gingrich, who had a 58% approval rating. Now the chart adds to 251%.

Suppose there are ten families. 6 have dogs, and 5 have cats (and 3 of the families have dogs and cats). You’re argument says that the proportion of families with pets is 110%, when it’s really 80%.

David Nieporent:
193% of what?

193% of the people who cast support votes. That is, the total number of support votes cast for the three candidates of interest was 193% of the people who cast them. (And, of course, the confusing number didn’t come from them. It’s the number you got when you chose to total things that don’t make very much sense to total.)

Is that a particularly good way to represent the data? No. Is it fundamentally wrong? No.

Consider, for example, a bar chart showing the number of voters who showed up in each of several counties compared to how many showed up at the previous election. Some will be less than 100% (fewer voters this election) some will be more than 100% (more voters this election). They now say “the average over the 10 counties was 120%”.

That’s not a meaningless number. It’s quite clear what it means. But it’s not 120% of anything. (Each percentage is of the voters in the previous election in that county but when you average percentages of different wholes, the result is still a percentage but no longer “of” anything in particular.)

All they did wrong was make their graphic confusing.

David Schwartz: An example of a pie chart where the total actually is meaningless might be a pie chart with one wedge for each of your three call centers and the size of the wedge showing how many minutes each center’s average call length is.

I guess I could see a second grader making this mistake.

The only valid use for a pie chart is to represent fractions of a whole. Not average minutes at various call centers, not approval ratings where people may approve of multiple public figures.

You could use a pie chart for one of these people, and plot a wedge for approve, disapprove, and neutral. Those would add to 100%. Or you could have a pie chart for data that showed how many voted for each candidate, where each person voting got one vote. You could use a pie chart, but I wouldn’t. Not unless there were only two pie segments, or three if the third were much smaller than the other two.

People who study human cognition, that is, the ability of a human to look at an object and understand it, will say that pie charts are one of the worst ways to try to represent data. Even for parts of a whole, charts with bars next to each other are better than bars stacked up to a height of 100%.

193% is

193% of what?

There is no reason a pie chart must represent slivers of a fixed whole,

No reason except that this is the purpose of a pie chart. If you want it to represent something else, you don’t use a pie chart.

An example of a pie chart where the total actually is meaningless might be a pie chart with one wedge for each of your three call centers and the size of the wedge showing how many minutes each center’s average call length is.

Yes, that would be another example of a situation in which nobody who understood what they were doing would use a pie chart, because it’s a misuse of the form.

An example of a pie chart where the total actually is meaningless might be a pie chart with one wedge for each of your three call centers and the size of the wedge showing how many minutes each center’s average call length is.

This graphic was bad because it confused people and poorly presented the information it did have. However, it did not present numbers that were actually incorrect nor did it violate some fundamental mathematical rule that pie charts must follow.

a circular chart divided into triangular areas proportional to the percentages of the whole

I think this simply means that the proportions of the number each wedge of the pie chart represents follows the visual proportions of the wedge sizes. The “whole” in one case being the whole chart and the other case the sum of the numbers, whatever it may be.

Ryan Waxx: I’m not seeing “must always add up to 100″ being a consensus.

Doesn’t this say what you think none of them say?

Ryan Waxx: * a circular chart divided into triangular areas proportional to the percentages of the whole wordnetweb.princeton.edu/perl/webwn

But not as funny as the time Fox put up a graphic with Frederick Douglass to illustrate a discussion of the Lincoln-Douglas debates.

Ryan Waxx: Henceforth, all criticism of LN is considered “whining”. Especially if you’re laughing at him. He doesn’t like that. Too many bad memories of the high school shower room, probably.

Dude, chill out. It was supposed to be a comic relief post after all the heavy-duty climate stuff. Have a brownie; I made ‘em myself.

What they needed here was a bar chart or maybe a Venn diagram, though in the latter case they would need to show how big the overlaps were and I don’t think they actually captured that data. At least it wasn’t published in the summary that Benjamin R. George links to above.

Actually, you know what they needed here? (*) A text chart:

Palin: 70%
Huckabee: 63%
Romney: 60%

That’s it. No charts, graphs, or diagrams. Graphics are supposed to convey additional information that is hard to see with just text. With only three numbers, the picture doesn’t add any information anyway. (I agree that a Venn Diagram would be appropriate if they actually were trying to show how the candidates’ support overlaps.)

(*) I leave out the real response: nothing, since the response to the question is actually stupid infotainment of no news value.

Wait, he’s serious?

Ryan Waxx: If you have a chart showing how people voted on something, but they were allowed to vote for more than one thing, then the total of the percentages will be greater than 100%.Yes, normally votes don’t work that way in this country.However many European countries do allow this form of voting.I had no idea that the VC liberal crowd was so provincial that they cannot even grasp the idea of a multiple-choice voting system or its results.If fox had normalized the pie chart wedges to total 100%, then they would have had to report different numbers on the chart than the actual percentages tuned out to be.It says something, that certain people here are so insanely rabid that if Fox doesn’t distort their charts to please the commenters’ jr-high-school understanding of charting, that the catcalls start.I wonder… had fox changed the numbers, would these same wise commenters then begin to gibber about how the numbers didn’t match the poll? Who cares?It’s Fox. Right?

I don’t think anyone (certainly not me) is saying this is intentional manipulation, it’s just a really dumb mistake by someone who doesn’t know how to make charts appropriately. It is misleading to represent it in the form of a pie chart, as it creates the impression that they asked each person who they favored most and were only allowed to pick one, rather than what apparently did happen, which is they asked each person whether they approved/disapproved of which candidate. A bar graph would be the far more appropriate representation. I also think it’s ironic that you accuse people of having a knee-jerk reaction to bash Fox when, based on your past comments, I think it’s far more likely that you are having a knee-jerk reaction to defend Fox and accuse other of having bias. (Even though this is just a local Fox affiliate- a kind of confusion that happens to be one of my pet peeves).

Nick

Thanks for your response. As you note, the chart is potentially confusing without the report. But for a TV viewer, the report wasn’t available. That’s why I don’t like the chart.

But you do, and that’s okay.

I actually like to sing “Kum-ba-ya.” Takes me back to Camp Sugar Grove near Pleasant Hill, Ohio. :)

On one hand if you did a pie chart with proportions of items with their gross number (instead of percent of total number), then that chart would not add up to 100 either(in most cases). This is a little more confusing since the gross numbers are themselves percentages.

On the other hand, the chart is measuring what is neither rivalrous nor complete. So, it doesn’t make sense to set them as proportions of a whole. Also, they should mention what that percentage is measured, both in chart and in the commentary.

As for me, I was just struck by how someone wrong about every political issue could also be wrong about something as simple as a pie chart… it’s just funny. If you want to come up with an actual example of another pie chart in which the size of the whole pie has absolutely no meaning, please go ahead, I will be very impressed. In the meantime, well, I guess you could find a way to use CNN to bolster your “argument” here. It is rather relevant.

Don’t you see that the choice of a pie chart over a bar chart is the important thing? Little things like screwing up an entire story from the ground up prove nothing. PROPER CHART CHOICE is where the hard news is at… Just ask RN.

Although I find it interesting that EV decided to report on this interesting news story, yet somehow he completely missed CNN’s manufactured story, and hilarious backpedaling after being called on it.

The more important question is, why does EV feel like he needs to dump on Fox? Trying to reestablish his academic bona fides after too much free market discussions on his blog?

Is this like the “Laugher Curve” baked into a pie?

What they needed here was a bar chart or maybe a Venn diagram, though in the latter case they would need to show how big the overlaps were and I don’t think they actually captured that data. At least it wasn’t published in the summary that Benjamin R. George links to above.

Incidentally, Fox Chicago got the source wrong as well: Opinions Dynamic rather than Opinion Dynamics.

Raise your hand if you learned what a pie chart is by reading some definition provided by a geomapping software company. And let me know if you use pie charts to compare unemployment rates in different states, or GDP growth over different intervals of time.

And yeah, I figured that the proportions are shown “correctly” — my point was that the “spiffy” presentation made the result hard to observe. Since the point of graphics is to make information easier to digest, that is another strike against the chart.

Face it, if you want to put this information in a graphic you use a bar graph. Much easier to understand and not dumb.

But I really don’t know why Waxx is having a temper tantrum about this. The last man standing against the chart Nazi hordes?

I presume that Waxx purportedly believes in an ideology that upholds self-reliance and objective standards of excellence and finds identity politics and victim-mongering disagreeable. And yet in this thread he is whining about the “chart czars” that are oppressing a local TV news station (because it so fashionable!), and in the Swiss thread he’s talking about the “mancession.” Funny that.