Descriptive statistics
Descriptive statistics for IB Analysis and Approaches HL: tables, graphs, centre and spread, and the effect of changing data, with IB questions.
Descriptive statistics is used to summarise a large amount of data with a few numbers and graphs. You learn to organise data into frequency tables, to draw and interpret histograms, cumulative frequencies and box-and-whisker diagrams, and to calculate the measures of central tendency (mean, median, mode) and of spread (range, quartiles, variance and standard deviation). You will also see what happens to the mean and the standard deviation if you change the data. In Paper 2 the graphic display calculator finds almost all the statistics, but the exam asks you to interpret them, so it is worth knowing what each one means.
Suggested order
Follow the sections in order: data and tables, graphs, central tendency, spread and effect of changing the data. At the end you have the IB exam questions grouped by type.
Basic percentages and fractions; the graphic display calculator.
Sections in this topic
Data, frequencies and tables
Population and sample, types of variable, absolute, relative and cumulative frequencies, and grouping data into classes. IB Analysis and Approaches HL.
3 worked examples Section 2Graphical representations of data
Bar charts, pie charts, histograms, cumulative frequency, quartiles and box-and-whisker diagrams, with IB examples. IB Analysis and Approaches HL.
3 worked examples Section 3Measures of central tendency
Mean, median and mode from raw data, frequency tables and grouped data, and which measure to choose when there are outliers. IB Analysis and Approaches HL.
3 worked examples Section 4Measures of dispersion
Range, quartiles, interquartile range, outliers, variance and standard deviation (σ and s), with tables and GDC methods. IB Analysis and Approaches HL.
3 worked examples Section 5Effect of changing the data
How the mean and standard deviation change when data are transformed, added or corrected. IB Analysis and Approaches HL.
3 worked examples End of topicIB exam questions: topic 12
IB exam questions on descriptive statistics: tables, histograms, cumulative frequency, mean, quartiles and standard deviation, with step-by-step solutions.
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