## Tips for drawing a normal distribution

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KNOW THY INFLECTION POINT

We have drawn a lot of sorry-looking normal distributions in our life. It’s a shape that’s hard to get down without a lot of practice.

Here’s a few tips that can make it easier.

- Start by marking out standard deviations on the x axis from -3 to +3
- At x=0, draw a point to be the top of the bell curve
- At ± 1 SDs draw points at about 5/8ths of the height
- At ± 2 SDs draw points at about 1/8th of the height
- At ± 3.25 SDs draw points on the X axis

Now, to get the bends right, we exploit the following cool fact: There is an inflection point at ±1 standard deviation. That is,

**At 1 standard deviation, the curve stops bending down and starts bending up. **

Draw through those points and voila, normal distribution!

You might be wondering if these tips are approximations or exact. The heights of the points are approximate but within 1-2% of the exact values. The inflection point at ± 1 SD is real. That’s right, the second derivative is 0 at exactly ± 1 standard deviation.

RELATED BUT DIFFERENT DSN POST

How to eyeball a standard deviation

R CODE FOR THE PLOTS

Gary Mcclellandsays:It is good for everyone to know that the inflection points of a normal curve are at +/- 1 sd, but all the drawing tips in the world won’t help my arthritic left hand draw a nice normal distribution. I use the computer!

July 29, 2019 @ 12:07 am