Before any average or chart, data has to be sorted into types and counted into tables. Then the real skill: reading tables, comparing two sets of data fairly, and knowing what the data can and cannot tell you.
Classify first (qualitative or quantitative, discrete or continuous), count with a tally, and read every fraction from the right row or column. To compare two data sets, always compare one average AND one measure of spread, and say what each means in context.
Section 01
Types of data and tally tables.
Open the lab and look at the frequency table: each value is listed once with how often it occurs. Move a frequency slider and watch the tally marks change, and check that the total at the bottom is always the sum of the frequencies.
Qualitative (categorical) data are words or categories: eye colour, favourite sport, type of car.
Quantitative data are numbers. They split into two kinds:
Discrete data are counted and can only take separate values: number of siblings, goals scored, shoe size (\(5\), \(5\tfrac{1}{2}\), \(6\) but nothing in between).
Continuous data are measured and can take any value in a range: height, mass, time, temperature.
Tally marks are grouped in fives: four strokes then a fifth stroke across them, so |||| means 5. The frequency is the total of the tally.
Worked example Classify the data
Classify each of these: (a) the colour of a car (b) the number of pages in a book (c) the time taken to run 100 m (d) a shoe size.
(a) Colours are words, not numbers: qualitative.
(b) Pages are counted, so only whole numbers are possible: quantitative, discrete.
(c) Time is measured and could be 12.3 s, 12.34 s, and so on: quantitative, continuous.
(d) Shoe sizes come only in fixed steps (whole and half sizes): quantitative, discrete.
Check: \(4 + 8 + 5 + 2 + 1 = 20\), the number of students.
Answer:
Pets
Tally
Frequency
0
||||
4
1
|||| |||
8
2
||||
5
3
||
2
4
|
1
Examiner trap
Always check that the frequencies add up to the total number of data values. A missing or double-counted value is the most common way to lose the mark for a frequency table.
Section 02
Two-way tables.
A two-way table sorts the same people by two things at once, for example gender and how they travel to school. Every row and every column has a total, and the grand total sits in the bottom-right corner. Fill in a missing cell by using any row or column where only one number is missing.
Worked example Complete a two-way table
60 students were asked how they travel to school. Complete the table.
Walk
Bus
Car
Total
Boys
9
28
Girls
14
Total
20
25
60
Girls total: \(60 - 28 = 32\).
Girls who walk: \(20 - 9 = 11\). Boys by bus: \(25 - 14 = 11\).
Boys by car: \(28 - 9 - 11 = 8\). Car total: \(60 - 20 - 25 = 15\).
Girls by car: \(15 - 8 = 7\). Check the girls' row: \(11 + 14 + 7 = 32\). It agrees.
Answer:
Walk
Bus
Car
Total
Boys
9
11
8
28
Girls
11
14
7
32
Total
20
25
15
60
Worked example Read fractions from the table
Using the completed table, find (a) the fraction of the girls who travel by car (b) the percentage of the bus users who are boys.
(a) 'Of the girls' means the girls' total, 32, goes on the bottom: \(\dfrac{7}{32}\).
(b) 'Of the bus users' means the bus total, 25, goes on the bottom: \(\dfrac{11}{25} = 0.44\).
\(0.44 \times 100 = 44\%\).
Answer: (a) \(\dfrac{7}{32}\) (b) \(44\%\)
Your turn
In a club of 50 members, 22 are adults. 30 members can swim, and 18 of the swimmers are children. How many adults cannot swim?
Read the words after 'of'. 'What fraction of the girls...' divides by the girls' total, not by the grand total of 60. Using the wrong total is the examiner's favourite trap in two-way tables.
Stage 1 · Learn
Check your understanding
Four quick checks. Each correct answer earns XP and records this skill on your profile.
Quick check+10 XP
Which of these is continuous data?
Quick check+10 XP
A tally reads |||||||| ||. What is the frequency?
Quick check+10 XP
In a group of 45 students, 20 are boys. 12 of the girls wear glasses. How many girls do not wear glasses?
Quick check+10 XP
Two runners' times: Ana has range 0.6 s, Ben has range 1.8 s. What does this tell you?
Section 03
Comparing data and its limits.
The lab shows test marks for two classes. Edit Class B's list so its marks rise, then make them more spread out, and see how the comparison statements change. A full comparison always has two parts.
Compare an average (mean or median): which set is higher or lower on average, in the words of the question (taller, faster, warmer).
Compare a spread (range, or interquartile range on Extended): a smaller spread means the data are more consistent.
Limits: a small sample, a biased sample (only asking one kind of person) or data from one day only cannot support a general conclusion. Correlation or a difference in averages does not prove a cause.
Worked example Compare two classes
Class A: mean test mark 62, range 40. Class B: mean test mark 58, range 15. Compare the marks of the two classes.
Average: \(62 > 58\), so Class A scored higher on average.
Spread: \(15 < 40\), so Class B's marks were more consistent (less spread out).
Write both comparisons in context, as full sentences.
Answer: Class A did better on average (higher mean), but Class B's marks were more consistent (smaller range).
Worked example Is the conclusion justified?
Sam asks 12 people in a gym how many hours of exercise they do each week. The mean is 6.5 hours. Sam says 'People in my town exercise for 6.5 hours a week on average.' Give two reasons why this may not be true.
Sample size: 12 people is a very small sample for a whole town.
Bias: people in a gym exercise more than most people, so the sample is not representative.
Answer: The sample is too small, and it is biased because only gym users were asked.
Examiner trap
With times, a LOWER mean is better (faster). With spread, a smaller range means MORE consistent, not 'worse'. Always say what the numbers mean in context, not just 'the mean is bigger'.
Stage 2 · Exam
Exam-style questions
Unlocks once the four checks above are done. Worth more XP, written to IGCSE Paper 2 and Paper 4 standard.
Finish the four checks above to unlock the exam questions
Exam style+20 XP
The table shows the drinks chosen by 120 people.
Tea
Coffee
Juice
Adults
30
25
15
Children
8
2
40
What percentage of the people who chose juice were children?
Exam style+20 XP
There are 80 students in a year group. 42 are girls. 35 students study French, and 23 of these are girls. How many boys do not study French?
Exam style+20 XP
Ana's 100 m times have mean 12.4 s and range 0.6 s. Ben's have mean 12.1 s and range 1.8 s. Which statement is correct?
Exam style+20 XP
15 people leaving a football match are asked if they like sport, and 14 say yes. Which conclusion is best supported?
Skill unlocked
Data classified, counted and compared.
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