This is an interesting question, but I doubt anybody (here or elsewhere) has an answer to it as it is formulated now. The question's wording is somewhat ambiguous:
"In existence" - how about diamonds that are well known to exist, but whose whereabouts are unknown? Such as the famous DBL diamond lost in Central Park? (Or lesser examples such as the Nizam, at a paltry 340 ct).
Or how to categorise diamonds that have been re-cut, such as the French Blue (now almost certainly the Hope)? Does it count in the "over 50 ct" category, or only in the "over 40"? (The French Blue was 69 ct, the Hope is 45 ct)
"cut and polished" is in direct contradiction to "mined" - so for example the Esperanza didn't count until last month? It was mined in June 2015, but it was only cut later in the year, and news of the complete cut (and auction sale) came out early in 2016. The rough was gem-grade from the start, and it was being finished in late October 2015 - when does it start to count? When the first cut is made? When the stone is totally polished? When it's available for sale or has been sold?
Still on the same contradiction, "mined and gem grade" - the Cullinan was cut into 105 smaller gems, but it was mined as a single stone. So is it part of the "over 3000 carats", where it's the only member, or does it have 105 entries ranging from 530 ct to undetermined (but almost certainly larger than 1 ct)?
All that is easy to solve (you simply need to take a stance on those issues) compared to the real difficulty posed by the question, which is largely due to two factors. Let's assume that we want to count items whose location is known, counted as cut, finished gems (Cullinan = 105 stones), categorised using their current weight. This is still extremely difficult:
1. Stock levels. There are cut diamonds in mines'safes (e.g. Argyle) and cutters' workshops, wholesalers and retailers, museums, banks' deposit boxes, auction houses and private homes. While each one of those locations (except possibly for the last 3) knows its levels of stock to a good level of detail, there is no aggregation source for any of that, and in fact some of these pieces of information are very closely guarded trade secrets: RTZ has created a sense of scarcity around its Argyle pink stones, and the last thing it wants is for the world at large to know there are 3 tonnes - or 15 million carats - of them in store. I made that number up, but I think you can see the problem.
2. Loose stones vs. jewellery pieces and melée vs. individual stones. The majority of diamonds existing today, are not and never were on the retail market as single items. They are in pieces of jewellery held in a billion stores, wholesaler vaults, banks' deposit boxes, museums and private homes, and most of them by number are small melée stones. I for one have no idea of how many of them we have in the house; I can with some mental effort tell you that we have only one diamond over 2 carats, but already with the "1 to 1.99" category, trouble starts. We have at least 4 that are almost certainly in this weight category, but they are set in pretty important jewellery dating from the 1930s, and I have no idea if 2 of them are above or below 1.50. There is no way I'll ever know how much they weigh precisely, and hopefully no-one will ever find out by destroying the pieces. The uncertainty increases exponentially with smaller sizes: we have at least 1,000 and likely less than 10,000 melée stones; I'm not going to count them, much less categorise them. And that's one household - though admittedly a household of jewellery nutters. Multiply by several hundreds of millions of stock-holding places, and you have a big quantification problem.
We can get an approximate idea of the distribution of larger stones (say 0.50 ct and above) by looking at what's for sale, but even that is skewed by a few things:
a. Larger diamonds are on the market for longer.
b. Smaller diamonds are not listed as single stones.
c. Not all diamonds appear on listing engines - whether retail or wholesale. Lower-end diamonds are sold by the gazillion already set in jewellery; contracts covering how many exist, but are not public domain, and higher end stones are sold by private treaty never even appearing on any "publicly visible" market.
d. A diamond may be listed by more than one seller.
e. Even if this is representative of the distribution, we still don't have a quantification of the aggregate amount that has been mined and cut since time immemorial... or how it is split across sizes: estimates of total production I can find are for rough, and the vast, vast majority of that rough will end as melée.
Anyway, here goes:
Base of over 500,000 stones for sale at the moment. (Round brilliants, D-Z only).
|up to 0.49|
|up to 0.99|
|up to 1.49|
|up to 1.99|
|up to 2.99|
|up to 3.99|
|up to 4.99|
|up to 5.99|
|up to 6.99|
|up to 7.99|
|up to 8.99|
|up to 9.99|
|10.00 and over|
|all but 24 are below 15 carat, and 15 of these above 20|
Do I believe the data? Well, I still think "70% below 1 carat" is an underestimate. Probably more like 90 or 95%. The rest is probably not bad, once it's adjusted for that underestimate. Which incidentally means that stones above 2 carats are about 1% and those over 5 carats are less than 0.1% of the total.