Estimation Contest: Guess the Total, Win a Book

I could, I suppose, attempt a quantitative estimate based on the size of the box. Instead, though, I'll make a wild-assed guess based on what I see and say that it will come to $73.19.

OK, based on past experience with buckets of change, I'll go with $120.94

The prospect of doing this analytically is appealing, especially since it would keep me from doing my job for quite a while.

In a move that will make my employer happy and me sad, I'll just guess. $60.42

I'll go with $82.47. I used to put my spare change in an old glove and it always wound up around $40.

$53.27. Just because.

But...but the ruler doesn't start at 1! What am I supposed to do, subtraction? Know how big a penny is? You're asking an awful lot from me, man.

In my experience, boxes full of change never come out to as much as you want them to. $35.

Having recently dealt with a similar amount of change, I'm going to guess $71.63.

Is this Price Is Right rules? If so, $1. If not, $25.

I recently cashed in a 24 oz. beer mug full of change before a trip, and it came out to somewhere around $70. I can't tell from the picture what the volume of the box is in fluid ounces, but it looks like it is probably bigger. I'll guess $95.37.

$90.43 'cause I just got a feeling.

My intuition says $135.06.

105.04

$73.58 based on estimated cubic inches (5" x 9" x 1.5") times a SWAG number of $1.09 per cubic inch.

Well, at least there's a method to my madness.....

I'm going with $110.25.

Hmmm. That bit of Tootsie Roll wrapper or whatever in the upper left corner makes me worry that there could be other pocket detritus in the box, but I'll be optimistic and bet that most of the box is coins of about the same denominations I see on the top layer, and that there's maybe, say 4 or 5 layers like this in the box. So.... still a pretty rough guess, but I'll say $124.

$83.20

Hmmm...I'm gonna go with 99.99.

$87.87

I'll go with $68.27

based on theCase's estimate of the size of the box, and on a slightly larger completely arbitrary number for the dollar value per cubic inch ($1.11 -- all ones!) I come up with $74.93

I think that the penny density is pretty high. $42.42

$81.54

116.53, maybe?

$63.79 in my guess.

$150.92

$59.40. I actually approximated the various coin ratios, found out the diameters of each coin to determine average diameter, used the same ratios to determine average coin value, etc.

And yet, after all that, when some of the numbers didn't look right, I changed one of them completely ad hoc. The number of significant figures is definitely much less than to the nearest cent.

$48.72

87.63

$80.81

$86.96. Method not revealed, but I promise to reveal it if I win :)

$100.00

$87.52 - I used to be quite good at this for UK coinage (Used to count the takings at PTA fundraisers) but am not familiar with the US coins, so I could be way out!

$57.13

My guess: $98.76

$144.

$64.90

83.50

66.66

94.33

One Dollar!

There's a largish gap between the 14th and 15th largest numbers, 74.93 and 80.81, which is just below the average of 83.30, so, 77.87. My analysis is foolproof, ha!, unless there are any more entries.

$21.56?

SWAG: $93.41

$57.75

82.28

and 17c Canadian that got given to you on accident

$45.70

$135.93
If I win, I'll explain my reasoning.

$166.32

$108.01

$200

$68.29

$60.87

$60.50 is my estimate.

Here's a harder question:

Does this picture contain enough information to accurately determine the exterior volume of the box?

Similar method to Case #13, but I disagree with his numbers. I get $84.60 with my best estimates of the numbers.

$77.43 my guesstimate.

I'll throw my hat in the ring and say $36.11.

I'll venture $37.43. Judging from the guesses, some people must think you've got a few gold doubloons buried in there.

$57.37

The banks around here won't do that any more :)

$72.72

:D

62.9...

Forty seven bucks

Whoops, I'm sorry, I've been in check writing mode and missed your specification re decimal.

My guess is $47.00

Doesn't look all that many layers deep but I could be wrong....$15.82

We'll begin with theCase's estimate of the size of the box, for a volume of 67.5 cubic inches, or 1106 mL. Assume that the box is filled only with quarters, and further assume that each quarter is a 1 mL sphere. (The actual volume of a quarter is 0.8 mL -- we overestimate the value of each coin, but underestimate the number of coins, and hopefully this cancels out.) Since a random packing of spheres is about 64% space-efficient, we expect the box to contain 707.84 coins, worth $176.96.

For absolutely no reason, or employment thereof, I'll say $147.42. Because I like the number.

I posted this on Livejournal's RSS feed instead of here, but I'll repost -- $53.09. Which is remarkably close to one up there for $53.27! It looks like about the same composition and density of coins I gave to the bank aboot a month ago.

Gally copy or no, I am still preordering the book.

I'd say $63.19

Not correcting for the oblique POV and assuming the top layer represents the remaining mass (by the way there seems to be a selection process against quarters in your coin box and you seem to be retaining pennies and dimes ... just sayin').
Depth of box ~ 42 mm, thickness of top layer of coins ~ 4.5 mm and value of top layer of coins $ 5.35.

I'm guessing $ 49.95 which to my eyes will be a bit light 'cause the oblique view underestimates the depth.

$127.13

I estimated an inside volume of 45 cubic inches, with a filling fraction of 0.9 (a perhaps-too-high estimate based on strong smectic ordering and polydispersity). It seems as if you have more pennies and quarters than other coins, which is often the case for me, but that turns out not to affect things much. The average coin has a volume of 0.036159 cubic inches and a value of $0.11350.

77.88

Twenty-four dollars and seventy-eight cents.

$78.97

I also do not pay attention closely enough. $ 24.78 is my one and only guess (even though it's repeated here twice).

$46.23.

My bank doesn't count change any more. If they like you they'll loan you their sorter box, so you can stack on the money more easily. I hope this is a west-coast only customer-hate thing.

It's $ 98.40 because the Volume of the heap equals 2.46 old gloves (actually mittens) with a capacity of $ 40, according to comment #4.

I guess the volume is about 500 cc, so the mass is about 2.5 Kg. Nickles are worth 1 cent/gram and dimes and quarters about twice that. There look to be more quarters than pennies, so I say $31.07

My telepathetic powers tell me there is $50.00 in that box.

So, there's ~$6 in quarters on the top layer, looking at the box, there's probably room for 13 'layers', if packed perfectly. Add in another $2 for dimes on each layer and $0.25 for pennies on each layer.

Each layer, assuming the top is representative, which it should be unless you shook it up a lot, that's $8.25/layer or $107.25

Packing is probably only 70% efficient so chop that by 30% to get our SWAG: $75.07

$140.05

$32.57

$327.32

I'm wagering that there's a stack of twenties hidden at the bottom (for no good reason).

I'm going to go with $65.00 :)

$105.69

Your contest reminded me of a rather famous experiment in which a couple of game theorist auctioned off a coin jar to their MBA students, which I posted about here:

http://albanyareamathcircle.blogspot.com/2009/08/coin-estimation-contes…

$115.22

$60.54. Well, each student in class guessed and that's what the average was. As good a system as any, yes??

Hmmm. I store my loose change in a Pringles can. This looks a little less than half the volume, and a Pringles can regularly yields about $110, so I'm going to guess... $52.37.

50.85 $

127.18

aaand, just on the off-chance that the box is considerably deeper than it looks: $210.14

$80.07

22.59

$67.54

$98.45

$28.52
total guess

$90.87

$37.55

$117.00

$64.80

$126.00 (Really rough but I counted around 40 quarters in what I called the top 1cm. Looks to be about the height of a tape measure (2"-3") so we'll say 10cm. 40Q + ~20 dimes + ~10 nickels + ~10 pennies = 12.60/cm)

$56

$67.56

183.31

$68.71

$123.47

The sorted list of values so far, up to comment 102 and up to data entry errors, is: [1, 15.82, 21.56, 22.59, 24.78, 24.78, 25, 28.52, 31.07, 32.57, 35, 36.11, 37.43, 37.55, 42.42, 45.7, 46.23, 47, 48.72, 49.95, 50, 50.85, 52.37, 53.09, 53.27, 56, 57.13, 57.37, 57.75, 59.4, 60.42, 60.5, 60.54, 60.87, 62.9, 63.19, 63.79, 64.80, 64.90, 65, 66.66, 67.54, 68.27, 68.29, 71.63, 72.72, 73.19, 73.58, 74.93, 75.07, 77.43, 77.87, 77.88, 78.97, 80.07, 80.81, 81.54, 82.28, 82.47, 83.2, 83.5, 84.60, 86.96, 87.52, 87.63, 87.87, 90.43, 90.87, 93.41, 94.33, 95.37, 98.4, 98.45, 98.76, 99.99, 100, 105.04, 105.69, 108.01, 110.25, 115.22, 116.53, 117, 120.94, 124, 126, 127.13, 127.18, 135.06, 135.93, 140.05, 144, 147.42, 150.92, 166.32, 176.96, 200, 210.14, 327.32]
99 entries, the mean is 82.4, median 74.9. The median difference between entries is 1.09. Just one duplication. Have also done some work.

$92.38

$141.28

I assumed the total volume of 9"x5"x1", a typical individual coin volume of 0.042in^3 (roughly that of the nickel), and equal parts penny, nickel, and dime, with twice as many quarters as pennies.

$103.57 or, for those of you who use the metric system, $103.57

$70.16. Just 'cause, really.

$47.98

$96.88

$134.36 is my guess

55.71

$138.26
I decided to estimate things on my own before reading any comments (and then was amazed to see 114 comments ahead of me), but my method, and most of my math came out remarkably close to that in #70

ONE MILLION DOLLARS!!!!!$

81.20 dollars

Uncle Al goes for $81.81.

$65.43

$54.40

$120.22

$37.37

The link in post 84 gives an experimental rate that MBA students averaged an estimate of $5.13 for a jar of coins worth $8.00. Taking that ratio with the statistics in post 107 (mean 82.4 median 74.9) gives 116.80 to 128.50 as a range of guesses. Splitting the largest gap in that vicinity (127.18 to 134.36) puts my guess at: 130.77.

$61.50.

I will explain my method if I win.
And probably if I don't.

Well, I calculate that the average coin should have a value of 10.5 cents and diameter of 20.7 mm. Estimating the volume and packing fraction, I get a fairly high value close to another guess. I'll round it up a bit to take a region of parameter guess space that is sparsely sampled: $182.72
Could work if there are some Sac dollars in there.

@67.74

89,53

$29.80

Assuming the visible ratio of the various coins is representative, and there's an inch layer of coins (hard to estimate depth), $77.77

$79.68

Excuse me, something I didn't consider. Change my guess to $63.37

I scoff at actually trying to estimate! Favorite numbers for the win!

10*e*pi=85.40

$101.78, by arguments to be revealed if I win.

$37.52

36.42.

$137.00

$17.46

$33.65

The sorted list of values so far, up to comment 139, up to data entry errors, and excluding the 1E6 outlier, is: [1, 15.82, 17.46, 21.56, 22.59, 24.78, 25, 28.52, 29.8, 31.07, 32.57, 33.65, 35, 36.11, 36.42, 37.37, 37.43, 37.52, 37.55, 42.42, 45.7, 46.23, 47, 47.98, 48.72, 49.95, 50, 50.85, 52.37, 53.09, 53.27, 54.40, 55.71, 56, 57.13, 57.37, 57.75, 59.4, 60.42, 60.5, 60.54, 60.87, 61.50, 62.9, 63.19, 63.37, 63.79, 64.80, 64.90, 65, 65.43, 66.66, 67.54, 67.56, 67.74, 68.27, 68.29, 68.71, 70.16, 71.63, 72.72, 73.19, 73.58, 74.93, 75.07, 77.43, 77.87, 77.88, 78.97, 79.68, 80.07, 80.81, 81.2, 81.54, 81.81, 82.28, 82.47, 83.2, 83.5, 84.60, 85.40, 86.96, 87.52, 87.63, 87.87, 89.53, 90.43, 90.87, 92.38, 93.41, 94.33, 95.37, 96.88, 98.4, 98.45, 98.76, 99.99, 100, 101.78, 103.57, 105.04, 105.69, 108.01, 110.25, 115.22, 116.53, 117, 120.22, 120.94, 123.47, 124, 126, 127.13, 127.18, 130.77, 134.36, 135.06, 135.93, 137, 138.26, 140.05, 141.28, 144, 147.42, 150.92, 166.32, 176.96, 182.72, 183.31, 200, 210.14, 327.32]
The mean is 83.72, standard deviation 44.90, geometric mean, 71.65, median 77.43 (hey, that's only 44 cents less than my guess, a lifetime ago, which was a deliberate attempt to follow the wisdom of the crowd as it existed at the time, in lieu of being able to ask steelykid to please count). The duplicate I thought was present was in fact the same number entered twice by the same person, so there were no duplicates and there still are not.

The median difference between entries in the sorted list is now 0.95. In the center two quartiles the average difference between entries in the sorted list is 0.69. A curious property of the list is that the median value has a difference of 2.36 from the entry immediately below it, which makes that gap currently a very good bet, on the dubious statistical hypothesis that the a priori probability density mirrors the crowd. My subjective choice is to define my Bayesian prior in terms of the crowd's current wisdom, and update when more crowd arrives. Not that I'm a good Bayesian.

If my impeccable statistical analysis contributes to someone winning, I want half of it.

i've counted pigs and boxen full of coins for vacation many times... my guess is $182.21

Ah heck, I'll play.

$83.94

-kat

$119.77

$60

$53.83

Hmmm...

$105.95 is my total off the wall guess.

$ 77.01

$ 128.91

$61.52

$62.26

$75.35 as a pure guess.

$128

27.00

97.80
Based on number of coins of diff. values on top layer and number of layers.

$74.01

The first four digits in my Air Force serial number 61 years ago. Now why do I remember that and cannot remember what I had for lunch yesterday?

A 79-year-old veteran. "Hi Mom!"

$30

$84.09

$77.22

I'm a sucker for this sort of game:

$110.88

47$

$93.80, twice what my last change haul brought at the bank.

$27.35

When faced with a tough decision, I always ask myself "What would Bill and Ted do?" $69.69

76.20.

>If my impeccable statistical analysis contributes to someone winning, I want half of it.

But Peter, how'm I gonna give you half? It's a manuscript.

102.67. From years of using quarters for laundry.

$112 because no one else had guessed it so far

67,18... how deep is the box anyway, the angle of the picture make it hard to guess :o

I am going to skew the median - my guess is $12, 398.41

$123.71

$51.23

Ah, the move @168 will not skew the MEDIAN value much at all.

$100 even.

$47.23

$52.53

We have a winner. Congratulations to Michael Day, comment #48.

$88.10

I don't know how trackbacks work, so I just wanted to tell you I put this in the Math Teachers at Play #14, over at Math Mama Writes