POTD: Approximately Normal

Approximately Normal
Bighorn Canyon, Montana

Trace the shape of the  hill in the foreground and what do you see? I see a curve approximating a normal probability distribution, a.k.a. Gaussian distribution, a.k.a. “bell-shaped curve” for those of you who remember grading on the curve. (Do they still do that?) This one doesn’t look much like it’s bell-shaped though. It’s flatter than the standard normal distribution (mean=0, standard deviation=1.0) from which the bell-shaped moniker was derived. This one appears to have a standard deviation of about 2.5 based on my crude guessing. What does all this mean? Nothing really except, to borrow an old adage, “you can take the boy out of statistics but you can’t take the statistics out of the boy.” Or at least it will take more than 14 years of retirement from the field of statistics for that to happen.

6 thoughts on “POTD: Approximately Normal”

    1. Spoken like a true photoshopper Kathy. Statisticians who developed (no pun intended) an interest in digital photography are probably the only group That were immediately comfortable with using histograms in Photoshop.

    1. The short answer is I don’t know. The long answer is I actually seriously pondered the hill’s kurtosis while sitting in the shade watching the changing cloud patterns moving across the land that afternoon. I wouldn’t hazard a numerical guess like I did with the standard deviation but I will say it looks platykurtic relative to a normal distribution. Your assignment for next time is to determine whether the apparent deviation from a standard normal distribution is better accounted for by kurtosis rather than by a larger standard deviation as I suggested in the original post.

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