# Compare two Medians

I'm taking an intro to data visualization class, but I don't have a strong foundation in statistics.

For now I'm trying to do something basic with bar graphs.

I basically want to plot the median price of two types of products. I'm trying to see how much the condition of an item affects its price and comparing it with another type of product.

median
price
(normalized
in some way)
|
|
|              A  B
|        B     [] []
|       []     [] []
|    A  []     [] []
|____[]_[]_____[]_[]______ condition (2 for now)
used      new


A is product type A. Let's say clothing for example. B is product type B. Let this one be guitar amps.

A typical piece of clothing can sell from \$20 to \$300. A typical new amp can sell from \\$100 to the thousands. As you can see, these products have wildly different price ranges.

For some products, the price between used and new drops only a little, because wear and tear doesn't matter much. For others (like clothing or cars), the price drops a lot.

If I just plot the actual median price, then only the comparison between used and new of the same product type would be useful. It would be hard to compare with the other category.

What sort of calculations can I apply to the data in order to make this useful for comparisons? Am I approaching this in the wrong way?

Data-wise, right now I have access to the individual prices of items with a specific selling condition.

I'd appreciate any help.

From a visualization perspective, bar graphs are the last plot you should use. Bar graphs should only be used for counts or percentage of totals. To plot medians you should consider comparative boxplots, comparative histograms, or line-plots with medians and standard errors - something with distribution information included in the plot.

Comparing across categories could be very tough, even in the clothes example, some brands of the same item will hold price better than other brands. You may have to stick with directly comparable products.

• Eventually I plan to move a way from bar graphs. I also plan to break down the products into three price ranges (for low-end and high-end stuff). The totally different categories are what make the comparisons interesting, I believe. I just really need to come up with a way to compare them. Apr 28, 2013 at 2:56
• Reference here to plotting means looks like a typo. In any case, box plots don't usually show means, unless means are added. The details of box plot implementations vary a lot between software, but plotting medians as default is standard. Apr 29, 2013 at 7:45

I think you face a problem that falls into the area of multivariate discrete statistics. As such, you could use you the tools of contingency tables.

You have a 3 categorical R.V. problem where A represents product, B price and C state of product respectively. I doubt whether median is a good statistic in your case since this is used for univariate statistics, what you compute is statistic based on marginals rather on the joint distribution you have. In any case summing along every row or column it will give you the marginals.

Alternatively, I recommend you checking visualization of a 3-way contingency tables, a topic explained briefly here in an R implementation called strucplot

• Thank you very much. The link doesn't seem to be working, but I'll try to find something similar. Apr 29, 2013 at 0:01
• @flameiguana: the link works for me, maybe it was just a temporary problem
– nico
Apr 29, 2013 at 12:42