Over the holidays I saw a normal curve on a TV commercial. We've seen histograms in a TV role before. The new car site TRUEcar.com contains three versions of their TV commercials displaying normal curves representing the distribution prices of chosen car models. The screenshot from one of their commercials, shown above, displays car prices as a normal distribution. The distribution shows the Manufacturer's Suggested Retail Price (MSRP) sitting about two standard deviations above the Average Paid price and, predictably, the TRUECar price about one standard deviation below the Average. This is repeated in another normal curve show above.

This is nice to see, but I have a problem with it. For what are undoubtedly graphic designer concerns, the prices are shown as points on the normal curve itself, but they should be more properly represented on a number line that tracks along under the curve. We've also seen this problem illustrated before in this blog: here and also here. The difficulty is in confusing the height of the curve with the size of the price. True, a careful look would show this is not the case, but I wonder how many people still misinterpret this placement, thinking of one price sitting at the top of a heap, and that price is the mean!

TRUEcar improves this somewhat on their website where you can select a given make, model, and year of a car and they will display a histogram of either the national or local comparison distributions of prices paid, as shown below. National comparison prices are much closer to bell-shaped than the smaller sample of local prices.

The horizontal extent of each histogram bar represents a small range of prices paid by a number buyers. This number determines the height of the bar. You can slide your cursor to highlight the histogram bars as they range from Below Market (under the 15th percentile), to Great prices (between the 15th and 45th percentiles), to Good prices (between the 45th and 70th percentiles, finally up to prices that are Above Market (here above the 70th percentile, not as extreme as they showed previously).Here again is the potentially confusing placement of reference prices on the curve rather than on the number line of prices below the curve.

Still, it's good to see normal curves on national TV.

Happy New Year to all.

## 4 comments:

My typically-OCD self has more of a problem with the placement of the prices themselves. The $37K price should be shown as more of an outlier than $40K. A difference of -$2004 appears to be 1 sd, while a difference of +$1409 appears to be 2sd.

That error would have been obvious if, as you suggested, the numbers were represented on the base.

Very good eye.

I totally missed the simple arithmetic! Thanks for noticing it.

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