I'm studying a course (Mathematics for Machine Learning). There's a quiz that is designed to test knowledge on using a model to fit data to predict frequencies in a Normal (Gaussian) distribution. The question is as follows:
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For the heights of a population, a model we may use to predict frequencies is the Normal (or Gaussian) distribution. This is a model for a bell-shaped curve, which looks like this,
It has the slightly complicated equation,
the exact form of which is unimportant, except that it is dependent on two parameters, the mean, μ, where the curve is centred, and the standard deviation, σ, which is the characteristic width of the bell curve (measured from the mean).
We can put these two parameters in a vector,
Pick the parameter vector p which best describes the distribution pictured.
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I picked the right answer. However, the real question for me is - while determining the Mean (geometrically - using just the graph) is quite straightforward, determining the standard deviation (geometrically - using just the graph) is a mystery to me. In the course lessons, the lecturer just picked two arbitrary points on the curve, as the standard deviation, but never explained how to pick/plot these points, i.e. how to know exactly where on the graph to plot them.
Many thanks in advance.