*Approximately Normal*

*Bighorn Canyon, Montana*

*2021*

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.

Kathy+EysterHAHAHAHA! 🙂 I thought you were going to compare the hill to a low-contrast histogram with an average brightness! 😉

lgbSpoken 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.

Jim McRaeWhat’s the kurtosis?

lgbThe 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.

Jim McRaeSociologists should never ask questions of statisticians for fear of being given an assignment.

lgbDon’t worry, it was just for extra credit.