RP 8: The price of a piece of LEGO

This idea comes from my friend Thomas. His son is like mine in that they both think LEGO are awesome, and they are correct. For some reason, Thomas decided to calculate the price per piece of LEGO in each set. To promote repeatability, I decided to do this also. Looking at the catalog at LEGO.com, I can get both the price of each set and how many pieces it has. Just a note, I looked at almost all of the Star Wars LEGO series and some other select themes. I didn't include any sets that had been marked down in price. I will put the first plot on down below, maybe this would be a good time for you to guess the average price per piece.

This is a plot of all the different themes mixed together.

From that plot, it seems that price per piece is fairly consistent. The slope of the linear function fitting the data gives $0.097 per piece. The one data point highlighted that seems of a little bit is the Republic Dropship with AT-OT. It is listed on LEGO as "exclusive" and is $0.14 per piece. A couple of those real expensive sets make it difficult to see the lower stuff. Let me zoom in on so that those sets are not included.

Here you can see I labeled a couple of the stray points. Another interesting thing is that the function that fits the data has a non-zero y-intercept. I guess this would mean that if you bought a LEGO box with zero pieces, it would still cost $6.18 (I guess that is for the packaging, instructions and stuff)

Do the different themes have different prices per piece? Here are the average prices per piece for different themes.

The cheapest per piece is the technic. This may be because the technic sets have lots of those really, really tiny pieces which are likely cheaper. Also, the bionicle sets are interesting. Most of these are for these big guys that all cost $12.99 and have "around" 50 pieces.

Finally, LEGO store has for sale individual lego pieces. I guess you could order all the pieces you need for a particular set instead of buying the set itself. I looked at about the first 100 pieces that were listed (not sure what order they were listed in) and I made a histogram of the prices.

I left off two points on this histogram. In the first 100 items, there was a piece that was $4.25 and there was a piece that was $0.54 (I left them off because they made the chart look odd). Including those two points, the average price per piece for the first 100 was $0.1795 with a standard deviation of $0.4238.

So, what is the point? I am really not sure. I have seen a lego program that lets you virtually build stuff, but it is really loud here right now and I can't find it.

UPDATE

I was thinking about this some more, one thing in my mind was that my friend said the average price per piece was something different than mine. I realized that I did not do the same thing he did. I fit a linear function to the set price vs. number of pieces data. In this fit, there is a non-zero price-intercept. What my slope says is: "If I increase the number of pieces by 1, what will the increase in the price be?". For just the star wars Lego sets, this value is $0.09951. In the bar graph above, I report the average price per piece as $0.11. This number is the price of the set divided by the number of pieces in the set and averaged for all sets.

If the linear function had a zero intercept, these two numbers would be the same. The first method is better because it takes into account the idea that there is some base cost to a lego set. If you had a lego set with just one piece, would it cost $0.11? (well, it would if you ordered it from the lego parts store - but it wouldn't be a 'set') I think this is a great example of the difference between slope and 'y/x' - which I find students often confuse.