IB Math AI SL — Mean, median, and mode

Key Idea: Topic 4.3 focuses on measuring the centre and spread of a dataset. The mean, median, and mode each describe the 'typical' value differently. Standard deviation measures how far values spread from the mean. Understanding how these statistics change when you transform the data (e.g., add a constant, multiply) is a key skill tested in exams.

✅ Measures of central tendency

✅ Measures of spread

Example: Grouped data mean: Class intervals: 0–10 (f=5), 10–20 (f=8), 20–30 (f=7). Midpoints: 5, 15, 25. x̄ = (5×5 + 8×15 + 7×25) / (5+8+7) = (25 + 120 + 175) / 20 = 320/20 = 16 Transformation: If x̄ = 50 and σ = 8, and each value is scaled by 1.1 then increased by 5: New mean = 50×1.1 + 5 = 60 New σ = 8×1.1 = 8.8

Use the GDC for standard deviation on real data — the manual formula is slow and error-prone. For skewed distributions: mean is pulled toward the tail, median stays near the centre. Use median when data is skewed or has outliers.

Paper 2 (GDC allowed): Enter all values in a list. Run 1-Var Stats to get x̄, σₓ, Sₓ, Q1, Q3 all at once. Write down the values you use. Paper 1: You may be asked to calculate the mean from a frequency table by hand — show the Σ(f×x) calculation step explicitly.