Statistics and probability cover data handling and chance. Students learn to present data, calculate averages, and solve probability problems using tree diagrams and Venn diagrams.
Mean = sum of values / number of values. Median = middle value when ordered. Mode = most frequent value. Range = max − min. For grouped data: estimated mean = Σfx / Σf (use midpoints). Cumulative frequency curve: plot upper boundary vs cumulative frequency. Read off median (50th percentile), Q₁ (25th), Q₃ (75th). IQR = Q₃ − Q₁. Box plots (box-and-whisker).
Histograms: frequency density = frequency / class width. Area of bar represents frequency. Scatter diagrams: plot bivariate data. Correlation: positive (uphill), negative (downhill), none. Line of best fit: straight line through the data showing the trend. Use to estimate values (interpolation = reliable; extrapolation = unreliable).
P(event) = favourable outcomes / total outcomes. P(not A) = 1 − P(A). Combined events: P(A and B) = P(A) × P(B) if independent. P(A or B) = P(A) + P(B) − P(A and B). Tree diagrams: multiply along branches (AND), add between branches (OR). Replacement vs without replacement affects probabilities.
When class widths are unequal, the y-axis shows frequency density (not frequency). Frequency density = frequency ÷ class width. The area of each bar (not the height) represents the frequency. To find the frequency from a histogram: frequency = frequency density × class width. This ensures fair comparison between classes of different widths.
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