Topic 1: Range of a data set Problem 1: Find the range of the data set {3, 7, 9, 12, 15}. Answer: Range = maximum - minimum = 15 - 3 = 12. Problem 2: Calculate the range of the data set {4, 8, 2, 10, 6}. Answer: Range = maximum - minimum = 10 - 2 = 8. Topic 2: Comparing measures of center and variation Topic 3: Using back-to-back stem-and-leaf displays to compare data sets Topic 4: Population standard deviation Problem 1: Calculate the population standard deviation for {2, 4, 6, 8}. Use σ = √[Σ(x - μ)² / N]. Answer: Mean μ = (2 + 4 + 6 + 8) / 4 = 20 / 4 = 5. Deviations: (2-5)² = 9, (4-5)² = 1, (6-5)² = 1, (8-5)² = 9. Variance = (9 + 1 + 1 + 9) / 4 = 20 / 4 = 5. σ = √5 ≈ 2.24.
  1. Find the mean = 5
  2. Fill out the table
    1. Add the last column 9+1+1+9
  3. Divide by n 20/4=5
  4. Take the square root sqrt(5)
 = 20 = 1.495
X X - mean (X-mean)^2
2 -3 9
4 -1 1
6 1 1
8 3 9
Topic 5: Sample standard deviation Same numbers as above.
  1. Find the mean
  2. Fill out the table
  3. Add the last column
  4. Divide by n-1 20/3=6.67
  5. Take the square root sqrt(6.67)
 = 1.607 Topic 6: Notation for the population mean, sample mean, population standard deviation, and sample standard deviation Topic 7: Comparing standard deviations without calculation Topic 8: Identifying the center, spread, and shape of a data set

Activity: