How do you calculate standard deviation on values that represent rates of change?
If you’re looking for the standard deviation of the change_value, your friend is right. Your calculation isn’t just paranoid; it’s wrong. Your delta and your median are being calculated on different bases, and it’s going to give you an invalid calculation. Look at it this way: you’re asking about the change values. They are a perfectly valid value all by themselves. The fact that they’re derived from something else is immaterial: they’re your dataset and you go with it. But your paranoia isn’t entirely unfounded, and it comes down to the question you really want to know. Let’s take a trivial data set: {1,2} and {1000, 1001}. The change_values are 2 and 1/1000, respectively. Which of these is more important to you, in your data set? If you think of them as representing returns on an investment, where I invested in dollars and you invested in Turkish lira, and you want to find the average improvement, what is it? You can say, “On average you two made just under 200%. Not bad.” We’re comp
