How Long is a Cheeto?

(TL;DR Summary: The average length of a Cheddar Jalapeño Cheeto is 1.68 inches.  Feel free to scroll down to the bottom for the graph).

My favorite snack is Cheddar Jalapeño Cheetos.  The fact that these things are only sold in 8.5 ounce bags or smaller in this area is a constant source of sadness for me.  Is the option to purchase a sack the size of a largish bean-bag chair too much to ask for, Frito Lay?  You know what? Forget the bags.  I should be able to call someone up and get this stuff dumped in my driveway in the same way you can have mulch delivered.

The back of the latest bag I wolfed down had this pic on the back:

So the claim here is that Cheetos are two inches long.  Being a connoisseur of sorts I knew that not all of these things are the same and, in fact, their sizes varied widely. Maybe they meant the average size of a Cheeto was two inches… Only one way to find out – I gots tuh get me another bag.  Woo hoo!

I called my wife, and she was nice enough to pick up another bag without saying “Ummm… weren’t you just eating a fresh bag of those when I left for the grocery store ten minutes ago?”, but there was a pause on the other end of the line exactly long enough to squeeze that sentence in.  She just said “Okay.”  I told her why, and she said “Will do.”  I’m pretty sure I heard the punctuation at the end of her reply, which is weird, right?  I’m… I’m sure it’s fine.

I opened the brand new bag this morning.  I fetched a notepad, a pen, the food scale, some parchment paper, a couple of bowls, a ruler and I got to work.

First, I weighed the bowls then filled them with the Cheetos, being as careful as I could not to break any – some would, of course, be broken in the bag already.  More on that later.  The front of the bag claimed 8 ½ ounces, or 240.9 grams.  The measured mass of the food in the bag was 241 grams, and the empty bag itself came in at 5 grams.  (FWIW: My food scale has a precision of 1g.  I have no idea what its accuracy is.  I’m betting it’s good enough, especially for this.)

Next, the fun part: counting and measuring, like, a billion Cheetos which is totally gonna take forever, right?  Actually, this part only took about 45 minutes.  I was super surprised by that.  There aren’t as may Cheetos in a bag as you might guess.

I made up a little chart and decided that measuring things to the nearest quarter-inch would be fine.  (Yep, I’m gonna mix English and Metric units here like a complete sociopath.  Make peace with that.)  I decided that anything below one inch would be considered a “crumble” and wouldn’t be measured by length, just mass, cuz the line has to be drawn somewhere. 

So this:

Was 1.75 inches and this:

Was 2 inches. 

So, yeah, only the overall lengths were measured, not the “path lengths” or “arc lengths” or what have you.   These things are twisty, turny chunks of uniquely shaped deliciousness and I wasn’t going to 3-D scan them.  Besides, if you are going to use these snacks to measure someone’s height like it says on the bag it’s not like you can straighten them out or anything.  It is what it is.

Here is the count:

Length   Number
1                30
1.25           43
1.5             45
1.75           35
2                40
2.25           26
2.5             20

The total number of Cheetos in the bag was 239, and the mass of the crumbles came in at 24 grams (10.0% of the total food mass).  Looking at these numbers, I wasn’t too surprised by the wide spread, but I was a little surprised at the high percentage of intact pieces.  I also expected the numbers to drop off more gradually on the high end.  I’m sure that there is such a thing as a three-inch Cheeto.  There has to be… there just has to.   I mean, what kind of God would create a world without the promise of them to comfort us in times of sorrow?

Here’s the breakdown:

Mean                       1.68
Median                    1.75
Mode                       1.50
Standard Deviation  0.46
Range                       1.50
Minimum                 1.00
Maximum                2.50
Sum                          401
Count                        239

And here we are, looking at an average length of 1.68 inches, not the solid two inches claimed on the bag.  The bag should say “21 Cheetos Crunchy Snacks = 2.94 +/- .80 feet end to end”, or, alternatively, “Between 20 and 34 Cheetos Crunchy Snacks = 3.5 feet end to end, with 25 or so being the most likely”.   Sure, the error bars are pretty big, these changes would make the bag virtually unreadable, and I’m being super unfair about the curvy-twisty thing, but, as everyone knows, cold hard data is at the heart of every tasty snack treat.

But the 1.68” thing is just on raw count.  I looked at the numbers a couple of different ways and got this:

While only 36% of the Cheetos were two inches and over, you can see that nearly half (47%) of the overall length consisted of the larger pieces.  What does that mean?  Well, it means that if you blindfold yourself and reached into the bag, you would have about a 1-in-3 chance of grabbing a 2” or bigger snack.  If you were to line them up end-to-end, though, and pointed to a random spot (not Cheeto…) in the line of Cheetos, there is about a 1-in-2 chance you would be pointing at a 2” or bigger piece.

By the way, the end-to-end length of all the Cheetos in this bag was about 33.5 feet (36 feet if you add the crumbles).

The grey columns show the distribution by mass instead of length, and that tells another story altogether.  The average (intact) Cheeto weighs about 0.91 grams, so my +/-1g scale was unsuited to measuring them individually.  I could, though, make some “first order” assumptions and proceed from there.  Assumption one – Cheetos can be modeled as cylinders and have a consistent length-to-width ratio.  Assumption two – all Cheetos have the same density.  These are “correct enough”.

Using these as guides I came up with the grey columns without needing to weigh a whole bag of Cheetos one by one, like I have time for that nonsense.  That data shows (fine… show… like that sounds right) that over two-thirds (67%) of the mass of the food in the bag consists of pieces two inches or greater.  Nice!

I eagerly await my Master’s Degree in Statistics from Frito Lay University.  It should come in the mail any day now.