Processing math: 100%
Problems
- (10 points) A teacher gives 5 students a multiple choice test, in which each problem is worth 1 point. The median and mean scores turn out to be 9 and 10 points, respectively.
- What is the minimum possible top score?
- What is the maximum possible top score?
- What is the minimum possible standard deviation?
- What is the maximum possible standard deviation?
- (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)
- (10 points) Textbook problem 1.12 (data)
- (10 points) Textbook problem 1.13 (data)