Chapter 3: Numerical Summary Measures

Question 1

stat vs parameter

Answer 1

stat: measure from a SAMPLE
parameter: measure from a POPULATION

Question 2

mean, trimmed mean median, mode

Answer 2

mean: summation of all data points over n (average)
= 1/N Σ xᵢ = E[x] = μ ( x̄ if sample)
trimmed: drop highest and lowest values, lessens impact of worst outliers
median: half point average
mode: value that appears most frequently

Question 3

variance formulas

Answer 3

population (use 1/N, μ and σ²)
1/N Σ (xᵢ–μ)² = σ²
1/N Σ (xᵢ²–μ²) = σ²

sample (use 1/(N–1), x̄ and S²)
1/(N–1) Σ (xᵢ–x̄)² = S²
1/(N–1) Σ (xᵢ²–x̄²) = S²

Question 4

standard deviation formulas

Answer 4

square root of varience

Question 5

Quartiles and IQR

Answer 5

points in data that signify quaters
IQR = Q3-Q1

Question 6

box plots and modified box plots

Answer 6

show max, min, Q1, Q3, Q2 (median)

mild outliers (dot): anything more than Q3+1.5 IQR or less than Q1–1.5 IQR
extreme outliers (star): more than 3IQR