Today at work Randy challenged everyone at lunch to estimate how much change was in his change jar. For the past decade or so he would throw his spare change into it. This weekend he’s going to Vegas to do a little gambling and would like to put his collection to “better use.” But before he turned it all in, we had a little fun trying to estimate its value.
He provided us with the weight that he measured using his bathroom scale (with the typical process of weight of jar and coins minus weight of just jar). That came to about 29 pounds. Then he also described how he didn’t really have any bias towards a particular coin, which is to say he hated all coins and just threw everything in. The other key piece of info was that his old roommate sometimes raided his coin jar for quick cash.
So we started by guessing what the distribution was of the coins. Our initial estimates consisted of: pennies 40%, nickles 23%, dimes 20%, and quarters 17%. Then we looked up the weight of each coin in grams and converted the weight of the coins to grams. Our first estimate came to a whopping $269.
Discussing our results, some felt the distribution of nickles was too low. Randy then brought in his bucket of coins and we decided to try a random sample set. So I took a handful and we counted them up. The following chart shows the exact calculations.
Doing the math on the white board caused several math errors to creep in, and so our first estimate came to $243.22, but should have come to what the graph shows: $245.97. In the end our flawed sample set proved to be quite good! After Randy took the change to the bank, the total came to a startling close result of $242.88! A difference of only 34 cents!
If you’re curious and want to do your own calculations, here are the values of the actual distribution which the change machine tallied: 2,543 Pennies, 317 Nickles, 551 Dimes, 562 Quarters, and 6 One Dollar coins. The following chart shows how close our estimates really were to the actual distribution: