Statistics: Displaying and Interpreting Data
What you must understand
Statistics questions ask you to classify data, choose and interpret displays, and summarise data with measures of centre and spread. You need to read and construct frequency tables, histograms, stem-and-leaf plots, dot plots, box plots and scatterplots; calculate mean, median, mode, range, quartiles and interquartile range; and describe association in bivariate data, including the line of best fit and correlation.
Traps that appear in questions
- Mean from a frequency table. Multiply each value by its frequency, add, then divide by the total frequency - not by the number of rows.
- Median position. For n values in order, the median is the ((n + 1) ÷ 2)th value; with an even n, average the two middle values.
- Quartiles. With small data sets, conventions vary; use the method taught in your course and state it. The interquartile range is Q3 − Q1 and measures the middle 50%.
- Outliers and the mean. A single extreme value shifts the mean strongly but barely affects the median, so the median is more resistant.
- Correlation versus causation. A strong correlation does not prove one variable causes the other.
- Reading graphs. Check the scale and axis labels; a broken axis can exaggerate differences.
Worked example
Data: 3, 5, 5, 7, 9, 11, 14. The mean is (3 + 5 + 5 + 7 + 9 + 11 + 14) ÷ 7 = 54 ÷ 7 ≈ 7.71. The median is the 4th value, 7. The mode is 5. The range is 14 − 3 = 11. Q1 = 5 and Q3 = 11, so the interquartile range is 6, describing the spread of the middle half of the data.
Rule of thumb
Order the data first, identify whether the question asks about centre or spread, and match the statistic to the display - medians and quartiles for box plots, means and frequencies for histograms.