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STATISTICS LAB
Learn it by playing it
Four short missions on live data: find the middle of an ordered row, weigh a frequency table into its mean, measure how spread out two classes are, then read a median straight off a cumulative frequency curve. When a mission glows green, read why it worked.
1234
Mission 1 of 4
Order up
Nine goal totals from nine matches, already in order: 3, 5, 5, 6, 7, 8, 9, 9, 10. Dial in the median - the value sitting exactly in the middle of the ordered list.
median = 0
Before you touch the dial: the median of the nine values is?
Currently dialled 0 - count in from either end of the ordered row until you meet in the middle.
Study notes
Classifying and tabulating data C9.1 / E9.1
Categorical data comes in words (favourite sport, eye colour); discrete data is counted in separate steps (number of brothers); continuous data is measured and can take any value in a range (height, time).
A tally table counts as you collect: one stroke per item, and every fifth stroke crosses the previous four, so a gate of five plus two strokes is 7.
The frequency is the total for each row or class - it answers 'how many?', not 'how big?'.
Group continuous data into classes that touch but never overlap: 10 < t <= 20 takes every value above 10 up to and including 20, so 20 lands here and 20.1 lands in the next class.
A two-way table shows two features at once, like gender against club choice. Row totals and column totals both add to the grand total, so any empty cell falls out by subtracting.
After completing a table, check one row total and one column total - if both add up, the table is almost certainly right.
Reading tables and comparing data sets C9.2 / E9.2
Before computing anything, read the title, the axis labels, the units and the key - most misreads come from skipping the key.
Watch the denominator in 'of the' questions: 'what fraction of the girls chose sport' divides by the number of girls, not by the whole group.
To compare two data sets you need two statements: one about an average (which set is higher or lower on average) and one about spread - the range at Core, the range or interquartile range at Extended.
A comparison uses comparative words tied to the context: 'Class Q scored higher on average and its marks were more consistent.' Listing the two numbers side by side is not a comparison.
Appreciate the restrictions: a sample that is small, unrepresentative or self-selected will not support a conclusion about everyone, and a chart with a truncated axis can exaggerate a small difference.
Mean, median, mode and range C9.3
Mean = total of the values / number of values. It uses every value, which is its strength and its weakness - one extreme value drags it.
Median = the middle value once the data is in order. With n values it sits at position (n + 1)/2; with an even count, average the two middle values.
Mode = the most frequent value. It is the only average that works for categorical data, and it answers 'most popular', not 'typical size'.
Range = largest - smallest. It measures spread, not centre, and one outlier can make it look wild.
From a frequency table, mean = sum of (value x frequency) / sum of frequencies: for 0,1,2,3 with frequencies 4,6,6,4 the mean is (0 + 6 + 12 + 12) / 20 = 30/20 = 1.5. Core data stays in a list or an ungrouped frequency table.
The mean need not be a possible value - 1.5 siblings is a perfectly good mean. Choose the average to fit the purpose: mode for most popular, median when outliers skew the data, mean when every value should count.
Charts that carry data C9.4 / E9.4
Bar charts show frequency against categories or discrete values; dual bar charts place two sets side by side and composite bars stack them, and both need a key.
Pie chart angle = frequency / total x 360 degrees. 30 cricket fans out of 90 students take 30/90 x 360 = 120 degrees. All the angles add to 360 degrees.
A pictogram draws repeated symbols, each standing for a fixed number stated in the key - a half symbol means half that number.
A stem-and-leaf diagram keeps the raw values: the stem holds the leading digits, the leaves are ordered smallest to largest, and the diagram is invalid without a key such as 1 | 2 means 12.
A simple frequency distribution lists each value with its frequency; read totals by adding the frequency column.
Whatever the chart, the first read is the same: title, axes, units, key.
Scatter diagrams and lines of best fit C9.5 / E9.5
A scatter diagram plots paired data, one point per pair, marked clearly with small crosses.
Positive correlation: as one variable rises, so does the other. Negative correlation: as one rises, the other falls. Zero correlation: no pattern. Correlation never proves that one variable causes the other.
A line of best fit is a single ruled line drawn by inspection - by eye, not point to point.
The line should extend across the full data set, need not pass through any plotted point, and should leave points roughly balanced on either side along its whole length.
Use the line to estimate: go up from the x-value to the line, then across to the y-axis. Estimates inside the data range are reliable; far outside it they are guesses.
Grouped data, cumulative frequency and histograms E9.3 / E9.6 / E9.7
Quartiles split ordered data into quarters: Q1 is a quarter of the way through, the median halfway, Q3 three quarters. Interquartile range = Q3 - Q1, and it ignores the extreme tails, so it is a sturdier measure of spread than the range.
For grouped data the mean is only an estimate: use the midpoint of each class, then mean estimate = sum of (midpoint x frequency) / total frequency. The modal class is the class with the highest frequency.
A cumulative frequency table adds the frequencies as you go, and each point is plotted at the UPPER boundary of its class, joined with a smooth curve.
Read the median from the curve at half the total frequency, Q1 at a quarter and Q3 at three quarters; percentiles work the same way at any percentage of the total. Go across to the curve, then down to the axis.
A histogram looks like a bar chart but the AREA of each bar is the frequency, because the classes can have different widths. The vertical axis is frequency density = frequency / class width.
So a class of width 20 with frequency 40 has frequency density 2, and a bar twice as tall means twice the frequency density, not necessarily twice the frequency.
EduTribe study notes - original material aligned to the Cambridge IGCSE Mathematics 0580 syllabus (2025-2027). Automated checks completed; not yet reviewed by an educator.