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Problems
- (5 points) Textbook problem 1.4
- (5 points) Show that std({kx})=|k|std({x}) by substituting into the definition. You'll need to use the properties of the mean.
- (10 points) Let {x} be a dataset consisting of N real numbers, x1,…,xN. Read the derivation in section 1.3.1 of the textbook that shows that the function f(μ)=∑i(xi−μ)2 is minimized when μ=mean({x}).
- Assume that N=4 and that x1≤x2≤x3≤x4. Show that the function g(μ)=∑i|xi−μ| is minimized when μ=median({x}).
- In at most two sentences, explain why the median is less sensitive to outliers than the mean using what you know about f(μ) and g(μ).
- (10 points) Textbook problem 1.11 (data, description)
- (10 points) Textbook problem 1.13 (data, description)
- (10 points) Textbook problem 1.15