Guess the Standard Deviation

1. Look at the histogram

Each round, you'll see a histogram of 500 data points drawn from a random distribution. The shape, spread, and center will vary wildly — normal, exponential, bimodal, and many more.

2. Guess the standard deviation

You have 5 seconds to type your estimate of the standard deviation. Think about how spread out the data looks. If the data spans roughly 10 to 30, the SD might be around 5. If it's tightly clustered, maybe 1 or 2.

3. Scoring

Your error for each round is: |log(your guess) − log(true SD)|

This means being off by a constant ratio matters, not a constant amount. Guessing 2 when the answer is 4 is the same error as guessing 4 when the answer is 8.

Your final score is the mean log error across all 10 rounds. Lower is better.

4. Tips

Look at the x-axis range. A histogram spanning 20 units has a larger SD than one spanning 5.
For a normal distribution, roughly 95% of data falls within 2 SDs of the mean. So if the data spans ~20 units, the SD is around 5.
Skewed distributions (exponential, log-normal) can be tricky — the long tail inflates the SD more than you might expect.
Don't overthink it — you only have 5 seconds! A rough estimate is fine.
If time runs out, whatever you've typed gets submitted. An empty box gives you a penalty.

5. What counts as a good score?