Statistics
Statistics tests collection, presentation and interpretation of data: averages, frequency tables, cumulative frequency, histograms, scatter graphs and comparing distributions. The exam expects a measure of average and a measure of spread when comparing two data sets.
Core ideas
- Mean = total of values ÷ number of values. From a frequency table, use class midpoints and Σfx ÷ Σf.
- Median: order the data; for n values the position is (n+1)/2. Lower quartile at (n+1)/4, upper at 3(n+1)/4; IQR = UQ − LQ.
- Modal class is the class with the highest frequency; the mode is the most common value.
- Cumulative frequency is plotted at the upper class boundary; the median is read at n/2.
- On a histogram, frequency = frequency density × class width.
- Scatter graphs show correlation, not causation; the line of best fit passes through the mean point.
Worked example
A grouped table has 20 students with marks 10–19 (frequency 4), 20–29 (6), 30–39 (7), 40–49 (3). Midpoints are 14.5, 24.5, 34.5, 44.5. Σfx = 58 + 147 + 241.5 + 133.5 = 580, so estimated mean = 580/20 = 29. The estimate assumes values are spread evenly within each class.
Traps
Using class limits rather than midpoints; plotting cumulative frequency at the midpoint; reading the median from a histogram as if it were a cumulative curve; claiming a strong correlation proves cause.