I started to make a set-up to find the variations from the “real” coins in my collection against the so-called standard value given by the mints.
Here is the graph for the mass of all my 1 euro cent coins in my collection
Diameters
Thickness
What do you think? Is it worth to continue, or would the interval beween highest and lowest measures value be enough? Where would input that into numista?
Interesting. So for weight you get 2.3g +1.7%, -3.4%. But that's just using the absolute lowest and highest and ignoring the quantities (i.e. ignoring the numbers of coins for each country) . I'd like to see all the data combined to get a true average and standard deviation. I'm guessing you'd end up with 2.3 g +/- 2%.
I did a similar thing very recently with US 1 cent coins (copper plated zinc, circulated with no/minimum wear). Here's the results:
I only have one coin per year for each country. The amount of coins per country is given after the Country on the X-axis. I use the number of coins to give me the average mass per country, which is then used in another system, where I compare the deviations against the average.
Never met a statistic I didn't like 😀 (oh wait … that's only if I exclude election days).
So, assuming the varation is evenly distributed about the mean, we conclude the euro cents are running a bit low on mass because they are a bit low on thickness?
Never met a statistic I didn't like 😀 (oh wait … that's only if I exclude election days).
So, assuming the varation is evenly distributed about the mean, we conclude the euro cents are running a bit low on mass because they are a bit low on thickness?
I don't think you can say that from the graphs shown. Only the max and min values of each country are shown. Let's say Ole measured the weight of 8 coins from Country A with the following values:
2.22
2.32
2.30
2.31
2.29
2.30
2.31
2.29
The 2.22 makes it appear Country A is very underweight but the average is 2.293 almost spot on to the standard of 2.3. Or, as you put it, the variation isn't evenly distributed about the mean in this case. Same goes for thickness.
Edit: You would also have to conclude the diameter is a bit high which would have a much greater affect on weight.
That's why I siad “assuming the variation is evenly distributed,” but that may still be wrong.
On the other point, need to take into account that each division in the diameter graph is only 0.1% of the standard, but on the thickness graph it is 3%.
Which makes sense … a planchet could be a little thicker or thinner than the standard, but the presses will make every coin the same diameter.
I can send you my data in Excel form, if you would like to play a bit? Please send me your email addresses!
Thank you, but I will pass.
All I need is one more distraction from the work I should be doing on Numista. 🙂
And … the stats on the Lincoln are interesting. COV of 0.8% is a bit lower than I expected, since we tend to hear “+/- 3%” which I assume applies to 3 sigma.
And the shape of the distribution to have a little high skew, but I guess that's just one coin, so it would take a bigger sample to know if it's real?
Yes it's skewed on the high end. I have to believe that the population is of a normal (bell-shaped) distribution so the mean +/- 3 standard deviation will encompass 99.7% of all coins.
The standard allowable variation is often quoted as +/- 4% on weight. I believe that to be true but in practice, as this shows, the actual variation is more like +/- 2%. It just means that the current minting process is well under control. The mint certainly doesn't want to scrap any coins.
So this is what it looks like with average of each country plotted:
Every country's average was below the 2.30g standard which seems odd to me.
Combining all the data of all the countries results in this. Not the normal distribution I was expecting but maybe makes sense since unlike the US 1 cent coins there's multiple production mints with separate operations.
So this is what it looks like with average of each country plotted:
Every country's average was below the 2.30g standard which seems odd to me.
Combining all the data of all the countries results in this. Not the normal distribution I was expecting but maybe makes sense since unlike the US 1 cent coins there's multiple production mints with separate operations.
Interesting that despite many more production locations, the COV is not much higher than what you had for the U.S. Lincoln (1% vs 0.8%). The bar chart almost looks like it has a shouder on the left side … which as you say, might not be unexpected if those data were predominantly one mint location that had some source of deviation.
Since the standard values for the standard of mass, diameter and thickness are quite different in actual numbers, the measured numbers will of course also be different, when taken down to the percents of the standard number:
Yes of course. The diameter is very easy to control tightly with a die/collar process so not surprising it has a relatively small variation. The mass is completely dependent on the blank making process including the initial sheet thickness and initial blank diameter. The final thickness is dependent on the variation in mass plus variation in minting pressures plus I would guess measurement errors from such a small size being measured.
But in the end your data shows the standards are being met for the 1 euro cent coin even with all the (allowable) variations:
