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Cambridge IGCSE Maths (0580) · Statistics
Mini-Lesson

Statistics

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.

Averages

Mean, median, mode & range

Four values summarise a data set:

  • Mean = sum of values ÷ number of values.
  • Median = middle value when the data are put in order (average the middle two if there is an even number).
  • Mode = the value that occurs most often.
  • Range = largest − smallest (a measure of spread, not an average).
Worked example

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.

Calculate

Your turn

1Find the mean of 4, 8, 7, 5, 6.
Hint: add them (4+8+7+5+6 = 30) then divide by 5.
Calculate

Your turn

2Find the median of 11, 4, 7, 2, 9, 4, 8.
Hint: order them → 2, 4, 4, 7, 8, 9, 11 (7 values, so the 4th is the middle).
Frequency tables

Mean from a frequency table

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.

Worked example — goals per match

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.

Calculate

Your turn

3Number of pets x: 0, 1, 2, 3 with frequencies f: 6, 9, 3, 2 (20 people). Work out the mean number of pets.
Hint: Σfx = 0×6 + 1×9 + 2×3 + 3×2 = 21, then ÷ 20.
Grouped data

Estimated mean of grouped data

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.

Worked example — times (minutes)

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.

Calculate

Your turn

4Mass m (g): 0<m≤20 (f=3, mid 10) · 20<m≤40 (f=7, mid 30) · 40<m≤60 (f=10, mid 50). Work out the estimated mean mass.
g
Hint: Σf·mid = 3×10 + 7×30 + 10×50 = 30 + 210 + 500 = 740, then ÷ (3+7+10)=20.
Cumulative frequency

Cumulative frequency, median & quartiles

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:

median at ½n · Q1 at ¼n · Q3 at ¾nread across from the CF axis, then down to the value axis · IQR = Q3 − Q1
value → cum. freq. median (½n)
Read the median at ½n, the lower quartile at ¼n and the upper quartile at ¾n.

Interquartile range (IQR) = Q3 − Q1. It measures the spread of the middle 50% of the data and ignores extreme values (outliers).

Calculate

Your turn

5From a cumulative frequency curve, the lower quartile is Q1 = 24 and the upper quartile is Q3 = 41. Work out the interquartile range.
Hint: IQR = Q3 − Q1 = 41 − 24.
Calculate

Your turn

6A cumulative frequency curve is drawn for 80 students. At what cumulative frequency value do you read across to estimate the median?
Hint: the median is at ½n = ½ × 80.
Box plots

Box-and-whisker plots

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.

minQ1 medianQ3max
Box = Q1 to Q3 (width = IQR), line inside = median, whiskers to min and max.

Reading spread: the width of the box is the IQR (Q3 − Q1); the whisker span (max − min) is the range.

Quick check

Quick check

?A box plot shows minimum 12, Q1 20, median 26, Q3 35 and maximum 48. What is the interquartile range?
Histograms

Histograms & frequency density

A histogram with unequal class widths uses frequency density on the vertical axis, so that the area of each bar equals the frequency.

frequency density = frequency ÷ class widthfrequency = frequency density × class width (area of the bar)
freq. density value (unequal widths) →
Height = frequency density; area of each bar = the frequency for that class.

Key trap: the bar height is not the frequency — it is the frequency density. Frequency = density × width (the bar's area).

Calculate

Your turn

7A class interval has width 20 and frequency 30. Work out the frequency density.
Hint: frequency density = frequency ÷ class width = 30 ÷ 20.
Calculate

Your turn

8A histogram bar has frequency density 2.4 and covers a class of width 5. Work out the frequency for that class.
Hint: frequency = frequency density × class width = 2.4 × 5.
Scatter diagrams

Scatter diagrams & correlation

A scatter diagram plots pairs of data to show a relationship (correlation) between two quantities:

  • Positive correlation — as one goes up, so does the other (points slope up).
  • Negative correlation — as one goes up, the other goes down (points slope down).
  • No / zero correlation — no clear pattern.
positive negative none
A line of best fit can be drawn through data with correlation to make predictions.

Careful: correlation does not prove one thing causes the other — it just shows they tend to change together.

Sort it

Which correlation?

Tap a relationship, then the box for the correlation you'd expect.

📈 Positive

📉 Negative

Pie charts

Pie charts

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:

angle = (frequency ÷ total) × 360°reverse: frequency = (angle ÷ 360) × total
all sectors add up to 360° bigger share = bigger angle angle = (part ÷ total) × 360°
Each sector's angle is proportional to that category's frequency.
Worked example

Of 40 people, 10 chose tea. Angle = (10 ÷ 40) × 360° = 0.25 × 360° = 90°.

Calculate

Your turn

9In a survey of 60 people, 15 chose football. Work out the angle of the football sector on a pie chart.
°
Hint: angle = (15 ÷ 60) × 360 = 0.25 × 360.
Match game

Match the statistic to its definition

Tap a statistic, then its matching definition.

Recap

Key points

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.

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