Key Idea: Topic 4.2 is about turning raw data into visual summaries. The three key displays are: frequency distributions (grouped data tables), histograms (bars show frequency density or frequency), cumulative frequency graphs (S-curves for finding medians and quartiles), and box-and-whisker plots (five-number summaries). Each display answers a slightly different question about your data.
✅ The five-number summary and quartiles
📊 Reading cumulative frequency graphs
Example: Data: 12, 15, 18, 20, 22, 25, 30, 35 Q2 = median = (20+22)/2 = 21 Q1 = median of {12,15,18,20} = (15+18)/2 = 16.5 Q3 = median of {22,25,30,35} = (25+30)/2 = 27.5 IQR = 27.5 − 16.5 = 11 Outlier fence: below 16.5 − 16.5 = 0 or above 27.5 + 16.5 = 44 → no outliers here.
When drawing a box plot: the box spans Q1 to Q3, the line inside is Q2, and the whiskers extend to the smallest/largest non-outlier values. For grouped data: use the midpoint of each class to estimate the mean; use the upper class boundary for cumulative frequency.
Paper 2 (GDC allowed): Enter data into lists and use 1-Var Stats to get Q1, Q3, and IQR automatically. The GDC also draws box plots. Paper 1: You may be given a completed cumulative frequency graph and asked to read off the median, Q1, or Q3 — show the horizontal and vertical lines on the graph for method marks.
IB-style question [7 marks]
The masses, in grams, of 50 apples picked from an orchard are grouped in the table below. Mass m (g): [80,100) → 6 apples; [100,120) → 14; [120,140) → 20; [140,160) → 8; [160,180) → 2. (a) Write down the modal class. (b) Estimate the mean mass of an apple. (c) Apples with mass at least 140 g are sold as 'large'. Estimate the percentage of apples that are 'large'.
Step by step:
(a) The modal class has the greatest frequency, which is 20.
(b) Estimate the mean from the class midpoints 90, 110, 130, 150, 170.
Multiply each midpoint by its frequency and add.
Divide by the total of 50 apples.
(c) 'Large' apples are in the classes [140,160) and [160,180): that is 8 + 2 = 10 apples.
Express the proportion as a percentage.
(a) [120, 140). (b) 124.4 g. (c) 20% are 'large'.