This mini-lesson covers Statistics for Cambridge IGCSE Mathematics (0580): mean, median, mode & range, frequency tables, grouped data & estimated mean, cumulative frequency (median, quartiles & IQR), box-and-whisker plots, histograms (frequency density), scatter diagrams & correlation and pie charts (Extended content included).
Honest heads-up: the quick-fire games here test your recall of facts, formulae and methods — not full written working. In the real exam you must show every step.
Work through each screen, answer the questions and collect ⭐ stars. Press Start.
Four values summarise a data set:
Data: 3, 7, 2, 9, 4, 6. In order: 2, 3, 4, 6, 7, 9.
Median = (4 + 6) ÷ 2 = 5. Range = 9 − 2 = 7.
Watch out: always order the data first before finding the median. The range is a measure of spread — it is not an average.
For a frequency table, the mean = Σ(f × x) ÷ Σf: multiply each value x by its frequency f, add these up, then divide by the total frequency.
Goals x: 0, 1, 2, 3 with frequencies f: 5, 8, 4, 3 (20 matches).
Σfx = 0×5 + 1×8 + 2×4 + 3×3 = 0 + 8 + 8 + 9 = 25.
Mean = 25 ÷ 20 = 1.25 goals.
Common slip: divide by the total frequency (Σf), not by the number of different values.
When data are grouped into class intervals, you don't know the exact values, so you estimate the mean using the midpoint of each class as x. Then mean ≈ Σ(f × midpoint) ÷ Σf.
0<t≤10 (f=4, mid 5) · 10<t≤20 (f=6, mid 15) · 20<t≤30 (f=10, mid 25).
Σf·mid = 4×5 + 6×15 + 10×25 = 20 + 90 + 250 = 360. Σf = 20.
Estimated mean = 360 ÷ 20 = 18 minutes.
Why "estimated": using midpoints assumes values are spread evenly in each class — so the answer is an estimate, not the exact mean.
A cumulative frequency is a running total of frequencies. Plot cumulative frequency against the upper class boundary and join the points with a smooth curve. For n values:
Interquartile range (IQR) = Q3 − Q1. It measures the spread of the middle 50% of the data and ignores extreme values (outliers).
A box-and-whisker plot shows five numbers: the minimum, lower quartile, median, upper quartile and maximum. The box spans Q1 to Q3 (the IQR) with a line at the median; the whiskers reach the smallest and largest values.
Reading spread: the width of the box is the IQR (Q3 − Q1); the whisker span (max − min) is the range.
A histogram with unequal class widths uses frequency density on the vertical axis, so that the area of each bar equals the frequency.
Key trap: the bar height is not the frequency — it is the frequency density. Frequency = density × width (the bar's area).
A scatter diagram plots pairs of data to show a relationship (correlation) between two quantities:
Careful: correlation does not prove one thing causes the other — it just shows they tend to change together.
Tap a relationship, then the box for the correlation you'd expect.
A pie chart shows how a total is split into categories. The whole circle is 360°, so each category's angle is its share of the total:
Of 40 people, 10 chose tea. Angle = (10 ÷ 40) × 360° = 0.25 × 360° = 90°.
Tap a statistic, then its matching definition.
Averages: mean = Σx ÷ n; median = middle (in order); mode = most common; range = max − min.
Frequency tables: mean = Σfx ÷ Σf; grouped data → estimated mean using midpoints.
Cumulative frequency: median at ½n, Q1 at ¼n, Q3 at ¾n; IQR = Q3 − Q1.
Box plots: min, Q1, median, Q3, max; box width = IQR.
Histograms: frequency density = frequency ÷ class width; area = frequency.
Scatter & pie: positive / negative / no correlation; pie angle = (part ÷ total) × 360°.
You've covered the Statistics essentials for Cambridge IGCSE Maths (0580). Press Finish to see your score.
You've worked through Statistics for Cambridge IGCSE Mathematics (0580). 🎉
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