This unit starts with data that has already been grouped: a table that kept the counts and lost the exact values. You will estimate a mean from it, find the class that holds the median, and read quartiles from a cumulative frequency curve.
Then the same summaries become pictures: box plots with a rule for outliers, and histograms whose bars have unequal widths, so that area, not height, shows how many values there are. The last two lessons compare two groups on centre and on spread, in context, and ask when a graph or an average is giving the wrong impression.
A graphic display calculator (GDC) is optional all the way through. Lessons 3 and 5 have a closed “With a GDC” section to open if you have one; everything else is done by hand.
The lessons, in order
- Lesson 1 · Estimating from grouped data Class boundaries, midpoints, the estimated mean from f × midpoint, the modal class, the median class by counting along the ordered values, and why grouped answers are estimates. Slide the values inside every class to see the band the mean must lie in, then walk along the ordered values to find the median class. Scientific calculator
- Lesson 2 · Cumulative frequency and quartiles Cumulative frequency tables, plotting at upper class boundaries, reading the median and quartiles from the curve or by interpolating, the interquartile range, and why it is steadier than the range. Pick a count on the vertical axis and read across and down to the value, then stretch the last class to see the range grow while the interquartile range holds still. No calculator
- Lesson 3 · Box plots and outliers The five-number summary, quartiles from the halves of an ordered list, the interquartile range, the 1.5 × IQR fences, drawing a box plot with a whisker and outliers, and reading what a box plot says. Slide the largest value past a fence to see it become an outlier while the box stays put, then move the quartiles to see equal quarters of different lengths. GDC optional
- Lesson 4 · Histograms with unequal widths Frequency density = frequency divided by class width, bar area as frequency, reading frequencies from a histogram, drawing from a table, and estimating the median by area. Switch one table between height-as-frequency and height-as-density, then change a class width to watch the height fall while the area stays the same. No calculator
- Lesson 5 · Comparing two distributions Comparing centre (median or mean) and spread (IQR or range), choosing measures that suit the data, the effect of an extreme value, and writing a comparison in context. Move and widen one box plot beside another, then grow one value in a short list and watch which summaries follow it. GDC optional
- Lesson 6 · Misleading graphs and reports Truncated axes, area and height in pictograms, how class width changes a histogram, averages of averages and percentages against counts, and the parts of a short statistical report. Move where a bar chart's axis starts to see the same bars tell different stories, then regroup one list to see the shape change. No calculator
Every lesson has a teacher page with the answers, the misconceptions each wrong answer reveals, discussion questions, differentiation and support for students learning in English, and extra questions in three tiers.