# Today I learned

## Statistics

While the following from statistics is too fundamental to be interesting, I struggled (and failed) to fully grasp it a few years ago. Hopefully, it will stick this time! Anyway, before I forget:

• Standard deviation is the square root of variance.
• Variance is the average of squared sum of differences between mean and observed values.
• Standard deviation is a measure of how spread out observed values are.
• Normal or Gaussian distribution is simply a bell curve, something that is fairly common in the real world.
• For such a distribution, 68% of the values lie within 1 standard deviation of the mean, 95% within 2 and 99.7% within 3.
• Standard normal disribution: is a (special) normal distribution which has a mean of 0 and standard deviation of 1.
• The y-axis of such a graph is just numbers but the x-axis is called the Z-score.
• You can convert a normal distribution to a standard normal distribution by calculating the Z-score as: ((observerd-value - mean) / standard-deviation).
• The area under the curve is 1.
• If you search online, you’ll find a table that, for a given Z-score, gives the area of the curve on the left of that score. That will answer things like, what’s the probability that a given value X is less than something.

Resources:

## D2L

• Extensive literature considers column vectors to be the default orientation of vectors, so does this book.