Monday, December 29, 2008

Average or Median: Which To Choose

A good number of readers and users of VGPC asked to see the average price for all games for each console and a chart to show the pricing history like we do for individual games. During some of the preliminary research into adding the feature I ran into an interesting dilemma. Do we show an average price or a median price? Which one we choose makes a big difference in the price we would show. Let me use the NES as an example. The average NES price is $17.55 while the median is $3.09. Why is there such a big difference?

We have prices for about 750 NES games and the vast majority of them sell for less than $10. From the chart below you can see how the game prices are distributed. The red bars show the number of games in a price range and the blue line is the cumulative percentage of games that sell below that price.
# of NES Games In Different Price Ranges

From the chart you can see that 60% of NES games sell below $4 and 80% sell below $10. There are about 60 games that sell for $20 or more, or about 7.8% of the total. These 60 games are the ones that skew the average so much higher than the median. Many of these games sell for well over $500. Nintendo World Championship alone adds $5.68 to the average price.

If we were to show the average price NWC and other expensive games would dominate the prices. For example, if NWC were to sell tomorrow for $6,000 the average NES price would jump from $17.55 to $19.87. But the median price would still be $3.09. Below is an example using the real average NES prices during the last 30 days. Between Dec. 4th and Dec. 5th the price jumped more than $2 because of a high priced game.
Average NES Price During December 2008

This same problem happens with other systems too. Newer systems like Xbox 360, Wii, and PS3 would see price spikes every Tuesday when new releases come out and older systems like SNES, N64, and Dreamcast would have big swings when rare games increase or decrease in price.

Because of this we are leaning towards using a median price instead of an average price when we start showing price charts for every console. What do you think?

The Median price for those who don't know is the cutoff where half the prices are above and half the prices are below that price.


Anonymous said...

the article makes it pretty clear median is the way to go. looking forward to it.

Gabe said...

JJ - I err on the side of wanting to know more information and would argue "both" if possible. In fact, because of my work focus, I sometimes would rather know perhaps the interquartile range (25th and 75th percentile) to get a gauge of the range in values. However, I can understand having to choose if you must.

If I were to choose, I would choose "median".

The reason is that averages are susceptible to influential and, sometimes not-so-meaningful, extreme values. If some product were sold at some outrageously incredible price, it would inflate the average value and, in a sense, artificially inflate the 'value' of the product. However, it's possible that extreme price or prices may not actually reflect the true 'value' of that product.

In contrast, medians are not as susceptible to extreme (low or high) values. They essentially will remain very similar (if not the same, depending on the circumstances).

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