📊 Statistics & Probability
Statistics and Probability questions test your ability to organise data, calculate measures of central tendency (mean, median, mode), compute standard deviation, draw and interpret statistical diagrams, and solve probability problems using tree diagrams and Venn diagrams. These are among the most scorable topics in Paper 2, often worth 8-10 marks per question.
Statistics and probability follow very predictable patterns in the exam. If you learn the formulas and practise the standard question types, you can score full marks consistently. The key is to show all working clearly — especially for mean and standard deviation calculations, where partial marks are awarded for correct method even if the final answer has a computational error.
Mean, Median, Mode
Mean is the arithmetic average: sum of all values divided by the count. For frequency tables, use \bar{x} = \frac{\Sigma fx}{\Sigma f}. For grouped data, use mid-values as estimates for each class interval. Median is the middle value when data is arranged in ascending order. Mode is the most frequently occurring value.
📊Measures of Central Tendency
Mean, median, and mode for ungrouped and grouped data.
\bar{x} = \frac{\sum x}{n}\bar{x} = \frac{\sum fx}{\sum f}\bar{x} = \frac{\sum f \cdot x_{\text{mid}}}{\sum f}\text{Median} = \text{value at position } \frac{n + 1}{2}\text{Mode} = \text{value with the highest frequency}📝Worked Example 1: Mean & Standard Deviation from Frequency Table
Goals scored in 20 matches: 0 (3 times), 1 (7 times), 2 (5 times), 3 (4 times), 4 (1 time). Find the mean and standard deviation.
📝Worked Example 2: Mean from Grouped Frequency Table
Marks: 10-19 (4 students), 20-29 (8 students), 30-39 (12 students), 40-49 (6 students). Find the estimated mean.
📝Worked Example 1b: Finding Missing Value from Mean
The mean of 6 numbers is 15. Five of the numbers are 12, 18, 14, 11, 20. Find the sixth number.
📝Worked Example 1c: Combined Mean
Class A has 20 students with mean mark 65. Class B has 30 students with mean mark 75. Find the combined mean for both classes.
📝Worked Example 1d: Effect on Mean When Adding/Removing Values
The mean of 10 numbers is 24. (a) If each number is increased by 5, find the new mean. (b) If each number is multiplied by 3, find the new mean. (c) If a new number 34 is added, find the new mean.
What the full chapter covers
Mean, Median, Mode
Standard Deviation
Cumulative Frequency & Box Plots
Histograms and Frequency Density
Probability
Pie Charts, Bar Charts, and Stem-and-Leaf Diagrams
Common Probability Distributions in Exam Questions
📊 More Worked Examples: Data Representation & Analysis
Probability Key Vocabulary
Statistics Scoring Strategy
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