Statistical Charts and Diagrams · Study Notes · Edexcel IGCSE 4MA1 Higher

Bar charts, pie charts, frequency polygons, scatter graphs (correlation + line of best fit), stem-and-leaf. Choose the right chart for the data type.

At a glance

Bar chart: discrete/categorical, bars DO NOT touch.
Histogram: continuous, bars TOUCH (separate subtopic).
Pie chart: angle = $\dfrac{f}{\text{total}} \times 360°$ .
Frequency polygon: plot at MIDPOINTS; join with straight lines.
Scatter graph: pairs of values; look for correlation.
Line of best fit: through middle of scatter.
Stem-and-leaf: stem + leaves + KEY.
Don't extrapolate beyond data.

What you’ll learn

Mapped to the Pearson Edexcel IGCSE 4MA1 syllabus (2026 onwards).

6.7 — Construct and interpret bar charts and pie charts.
6.7 — Construct frequency polygons for grouped continuous data.
6.7 — Construct and interpret scatter graphs; describe correlation; draw line of best fit.
6.7 — Construct and interpret stem-and-leaf diagrams.

Bar charts and pie charts

▼

Bar = discrete with gaps. Pie = sectors summing to $360°$ .

Bar chart. For DISCRETE/categorical data.

Each bar = one category.
Bar height = frequency.
Bars do NOT touch (gap between).

(Histograms are different — for continuous data with frequency density on the y-axis. Bars touch.)

Pie chart. Circle representing the whole. Each category gets a sector.

$\text{Angle} = \dfrac{\text{frequency}}{\text{total}} \times 360°$

Worked example. 60 students. Football 30, tennis 20, hockey 10.

Each student: $360°/60 = 6°$ .
Football: $30 \times 6 = 180°$ .
Tennis: $20 \times 6 = 120°$ .
Hockey: $10 \times 6 = 60°$ .
Sum: $180 + 120 + 60 = 360°$ . ✓

Each sector angle is the category's share of the total, scaled to 360°.

Drawing tip. Use a protractor; draw radii precisely. Label each sector with the category and either the frequency or the percentage.

Edexcel tip. Most pie chart questions on 4MA1 are about computing angles, not drawing. Show the formula step.

Bar: discrete, gaps.
Pie: angle = freq/total × 360.
Always check angles sum to 360.
Don't confuse bar with histogram.

Frequency polygons

▼

Midpoints + straight lines.

A frequency polygon is for grouped CONTINUOUS data.

Construction:

Find the midpoint of each class.
Plot points: $x$ = midpoint, $y$ = frequency.
Connect with STRAIGHT lines.

Worked example. Heights: $150 \le h < 160$ (5), $160 \le h < 170$ (12), $170 \le h < 180$ (8).

Midpoints: 155, 165, 175.
Plot: $(155, 5), (165, 12), (175, 8)$ .
Connect with straight lines.

Why midpoints? They represent the "average" value of each class.

Use case. Frequency polygons make it easy to COMPARE two distributions on the same axes — overlay them.

Edexcel tip. Common confusion:

Frequency polygon: MIDPOINTS, straight lines, plots FREQUENCY.
Cumulative frequency: UPPER BOUNDS, smooth curve, plots CUMULATIVE frequency.

Different chart, different points, different y-axis.

Plot at midpoints.
Connect with straight lines.
y-axis = frequency (raw).
Great for comparing distributions.

Scatter graphs and correlation

▼

Plot points; describe direction + strength.

A scatter graph plots pairs of values $(x, y)$ from observations.

Use case. Look for a relationship between two variables.

Correlation describes the trend.

Direction:

POSITIVE: as $x$ increases, $y$ increases (rises left-to-right).
NEGATIVE: as $x$ increases, $y$ decreases.
NONE / NO correlation: points scattered randomly.

A line of best fit fits a clear positive or negative trend; scattered points show no correlation.

Strength:

STRONG: points close to a line.
MODERATE: clear trend with some scatter.
WEAK: rough trend, lots of scatter.

Worked example. Hours studied vs test marks. Points trend upwards and cluster reasonably tight.

Description: STRONG POSITIVE correlation. As study hours increase, marks tend to increase.

Line of best fit. Straight line through the middle of the scatter — roughly equal points above and below.

Predictions from the line. Read off vertically from a given $x$ value.

Caveat. Predictions are only reliable WITHIN the range of the data. Don't extrapolate (extending beyond data).

Worked example. Data covers 1–8 study hours. A prediction for 7 hours is fine. For 20 hours: meaningless.

Causation vs correlation. Correlation tells you the variables MOVE together. It does NOT prove one CAUSES the other.

Edexcel tip. Mark scheme requires BOTH direction AND strength. "Negative correlation" alone misses a mark; "strong negative correlation" gets it.

Direction + strength.
Line of best fit: through the middle.
Predictions: only within data range.
Correlation ≠ causation.

See the full worked example for statistical charts and diagrams →

Stem-and-leaf diagrams

▼

Compact display preserving raw data. Always include a KEY.

Stem-and-leaf displays raw numerical data compactly while preserving the original values.

Stem: the higher digits.
Leaves: the last digit(s) of each value.

Worked example. Marks: 13, 15, 18, 20, 22, 24, 26, 27, 31, 35.

1 | 3 5 8
2 | 0 2 4 6 7
3 | 1 5

Key: 1 | 3 means 13

The key is essential — without it the diagram is ambiguous.

Reading off averages.

Total: count leaves. Here, 10.
Median: position $(n+1)/2 = 5.5$ , so average of 5th and 6th. Sorted (already in order): 13, 15, 18, 20, 22, 24, 26, 27, 31, 35. Median = $(22 + 24)/2 = 23$ .
Mode: most common leaf with the same stem (no repeats here, so no mode).
Range: max − min = $35 - 13 = 22$ .

Back-to-back stem-and-leaf. Compare two datasets: leaves on the left increase right-to-left.

Edexcel tip. Always include a KEY. Mark scheme: B1 for key, M1 for diagram structure, A1 for correct leaves.

Stem = higher digits, leaves = last digit.
ALWAYS include a key.
Preserves raw data.
Easy median + mode.

See the full worked example for statistical charts and diagrams →

Quick recap

Bar chart: discrete with gaps. Pie chart: angle = freq/total × 360.
Frequency polygon: midpoints, straight lines.
Scatter: describe direction AND strength of correlation.
Line of best fit: through middle; predictions within data range only.
Stem-and-leaf: stem + leaves + KEY (essential).
Match the chart to the data type.

Memorise this

Verbatim phrases and definitions Edexcel mark schemes credit.

Pie angle = $\dfrac{\text{frequency}}{\text{total}} \times 360°$ .
Frequency polygon: plot at MIDPOINTS.
Correlation: state DIRECTION + STRENGTH.
Line of best fit: through the middle, equal points each side.
Stem-and-leaf KEY: 'a|b means ab.'

How it’s examined

Charts and diagrams appear across both papers. Pie chart, scatter graph + correlation, and frequency polygon are most common. Examiner reports flag: (1) correlation answers without strength, (2) frequency polygon at wrong points, (3) stem-and-leaf without key, (4) extrapolating from line of best fit.

Sources: Pearson Edexcel International GCSE Mathematics A 4MA1 specification (2026 onwards); 4MA1 Examiner Reports — Jan and May/Jun 2022-2024 series; Past Papers — 4MA1/1H May/Jun 2024. Last reviewed 2026-05-07.

Step-by-step solutions to past-paper-style questions on statistical charts and diagrams, written exactly the way a tutor would explain them at the board.

1Build a pie chart
Foundation• pie chart
▼
Question
60 students. Sport choices: football 30, tennis 20, hockey 10. Find pie chart angles.
Step-by-step solution
1. Step 1
  Each student gets $360°/60 = 6°$ .
2. Step 2
  Football: $30 \times 6 = 180°$ . Tennis: $20 \times 6 = 120°$ . Hockey: $10 \times 6 = 60°$ .
3. Step 3
  Check sum: $180 + 120 + 60 = 360°$ . ✓
Answer
Football: $180°$ , Tennis: $120°$ , Hockey: $60°$
2Scatter graph: correlation
Higher• Adapted from 4MA1/1H May/Jun 2024 Q14• scatter, correlation
▼
Question
Data on hours studied vs test marks shows points trending upwards. Describe the correlation.
Step-by-step solution
1. Step 1
  Points trend upwards as $x$ increases — POSITIVE correlation.
2. Step 2
  If points cluster tightly around the trend → STRONG. Loosely → WEAK.
Answer
Strong/moderate POSITIVE correlation: as hours studied increase, marks increase.
Examiner tip
Always state DIRECTION (positive/negative) AND STRENGTH (strong/weak/moderate). Mark schemes credit both.
3Line of best fit and prediction
Higher• line of best fit
▼
Question
Draw a line of best fit. Use it to predict mark for a student studying 7 hours.
Step-by-step solution
1. Step 1
  Line goes roughly through the 'middle' of the points — equal points above and below.
2. Step 2
  Read up from $x = 7$ to the line, then across to the $y$ -axis.
Answer
(Whatever the y-value is at $x = 7$ on the line — e.g. 75 marks).
Examiner tip
Show construction lines on the graph. Mark scheme: M1 for line, A1 for reading.
4Frequency polygon
Higher• frequency polygon
▼
Question
Heights: $150 \le h < 160$ (5), $160 \le h < 170$ (12), $170 \le h < 180$ (8). Construct a frequency polygon.
Step-by-step solution
1. Step 1
  Plot points at MIDPOINTS, height = frequency: $(155, 5), (165, 12), (175, 8)$ .
2. Step 2
  Connect with STRAIGHT lines.
Answer
Three points connected with straight lines.
Examiner tip
Frequency polygon: midpoints, straight lines. (Cumulative frequency: upper bounds, smooth curve. Different.)
5Stem-and-leaf median
Foundation• stem-and-leaf
▼
Question
Stem-and-leaf: 1|3 5 8; 2|0 2 4 6 7; 3|1 5. Find the median.
Step-by-step solution
1. Step 1
  Total: $3 + 5 + 2 = 10$ values.
2. Step 2
  Median is between 5th and 6th values. List: 13, 15, 18, 20, 22, 24, 26, 27, 31, 35.
3. Step 3
  5th = 22, 6th = 24. Median = $(22 + 24)/2 = 23$ .
Answer
Median = $23$
6Why a pie chart's percentages cannot be right [1 mark]
Getting started• Paper 1H/2H style — 1 mark• pie charts, interpreting diagrams
▼
Question
A newspaper prints a pie chart with four sectors labelled $30\%$ , $25\%$ , $35\%$ and $20\%$ .

Give a reason why the pie chart cannot be correct. [1]
Step-by-step solution
1. Step 1
  Add the percentages.
  $30 + 25 + 35 + 20 = 110$
2. Step 2
  B1 The sectors of a pie chart make up the whole, so the percentages must add up to exactly $100\%$ . These add up to $110\%$ .
Answer
The percentages add up to $110\%$ , not $100\%$
Examiner tip
Examiner tip: A reason must say what is wrong and why: here, the total and what it should be.

Common mistake: Writing "the sectors are the wrong size" without saying why. Quote the total, $110\%$ , to make the reason precise.
7Putting boundary values into grouped classes [2 marks]
Getting started• Paper 1H/2H style — 2 marks• tabulation, grouped data
▼
Question
The masses of some parcels are to be recorded in a table with the classes $0 < m \leqslant 20$ , $20 < m \leqslant 40$ , $40 < m \leqslant 60$ and $60 < m \leqslant 80$ , where $m$ is the mass in kg.

(a) Write down the class that contains a parcel of mass $40$ kg. [1]

Here are the masses, in kg, of $10$ parcels.

12, 40, 55, 20, 63, 38, 41, 80, 27, 60

(b) Work out the frequency for the class $40 < m \leqslant 60$ . [1]
Step-by-step solution
1. Step 1
  B1 (a) $40 < m$ means $40$ is not included in the third class, but $m \leqslant 40$ means $40$ is included in the second. So $40$ kg goes in $20 < m \leqslant 40$ .
2. Step 2
  B1 (b) The masses greater than $40$ and less than or equal to $60$ are $55$ , $41$ and $60$ . The parcel of $40$ kg is not included; the parcel of $60$ kg is. The frequency is $3$ .
Answer
(a) $20 < m \leqslant 40$ (b) $3$
Examiner tip
Examiner tip: Read the inequality signs at both ends of the class. The strict sign ( $<$ ) excludes the boundary; the sign $\leqslant$ includes it.

Common mistake: Counting $40$ in the class $40 < m \leqslant 60$ (giving $4$ ), or leaving out $60$ (giving $2$ ).
8Comparing proportions from a dual bar chart [3 marks]
Building confidence• Paper 1H/2H style — 3 marks• bar charts, interpreting diagrams, proportion
▼
Question
A dual bar chart shows the numbers of boys and girls in a drama club from Year 10 and from Year 11.

Year 10: $14$ boys and $21$ girls.

Year 11: $24$ boys and $24$ girls.

Which year group has the greater proportion of girls? You must show your working. [3]
Step-by-step solution
1. Step 1
  M1 Find the proportion of girls in Year 10.
  $\frac{21}{14 + 21} = \frac{21}{35} = 0.6$
2. Step 2
  M1 Find the proportion of girls in Year 11.
  $\frac{24}{24 + 24} = \frac{24}{48} = 0.5$
3. Step 3
  A1 $0.6 > 0.5$ , so Year 10 has the greater proportion of girls.
Answer
Year 10 ( $0.6$ compared with $0.5$ )
Examiner tip
Examiner tip: "Proportion" means a fraction of the group, so each count must be divided by its own group total. Percentages ( $60\%$ and $50\%$ ) are equally acceptable.

Common mistake: Answering Year 11 because $24$ girls is more than $21$ girls. Year 11 has more girls, but a smaller proportion of its members are girls.
9From a bar chart with a missing bar to pie chart angles [4 marks]
Building confidence• Paper 1H/2H style — 4 marks• bar charts, pie charts, tabulation
▼
Question
A bar chart shows the numbers of visitors to a museum on five days. There were $90$ visitors altogether.

Monday: $12$ ; Tuesday: $20$ ; Wednesday: bar missing; Thursday: $27$ ; Friday: $15$

(a) Work out the number of visitors on Wednesday. [1]

The information is to be shown in a pie chart.

(b) Work out the angles of the sectors for Thursday and for Wednesday. [3]
Step-by-step solution
1. Step 1
  B1 (a) Subtract the known days from the total.
  $90 - (12 + 20 + 27 + 15) = 90 - 74 = 16$
2. Step 2
  M1 (b) Each visitor is represented by
  $360 \div 90 = 4^{\circ}$
3. Step 3
  A1 Thursday:
  $27 \times 4 = 108^{\circ}$
4. Step 4
  A1 Wednesday:
  $16 \times 4 = 64^{\circ}$
Answer
(a) $16$ (b) Thursday $108^{\circ}$ , Wednesday $64^{\circ}$
Examiner tip
Examiner tip: Check all five angles add up to $360^{\circ}$ : $48 + 80 + 64 + 108 + 60 = 360$ . The Wednesday angle follows through from your answer to (a).

Common mistake: Using $360 \div 5$ (the number of days) instead of $360 \div 90$ (the number of visitors).
10Frequencies in algebra, and one known sector [5 marks]
Stretch• Paper 1H/2H style — 5 marks• pie charts, forming equations
▼
Question
A survey asked some people which of four phones, A, B, C or D, they own. The frequencies were

A: $x$

B: $2x - 6$

C: $x + 10$

D: $16$

In a pie chart of the results, the sector for D has an angle of $48^{\circ}$ .

Work out the angle of the sector for B. [5]
Step-by-step solution
1. Step 1
  M1 $16$ people are shown by $48^{\circ}$ , so each person is $3^{\circ}$ and the total number of people is
  $360 \div 3 = 120$
2. Step 2
  M1 The frequencies add up to the total.
  $x + (2x - 6) + (x + 10) + 16 = 120 \quad\Rightarrow\quad 4x + 20 = 120$
3. Step 3
  A1
  $x = 25$
4. Step 4
  M1 The frequency for B is $2 \times 25 - 6 = 44$ .
  $44 \times 3$
5. Step 5
  A1
  $= 132^{\circ}$
Answer
$132^{\circ}$
Examiner tip
Examiner tip: The known sector gives the scale ( $3^{\circ}$ per person), and the scale gives the total. Check: frequencies $25$ , $44$ , $35$ and $16$ add up to $120$ .

Common mistake: Setting the frequencies equal to $360$ . The frequencies add up to the number of people; only the angles add up to $360^{\circ}$ .

Question 1
Paper 1H/2H style — 1 mark1 mark
In a pictogram, one symbol represents $6$ cars.

Write down the number of symbols needed to show $15$ cars. [1]
Model answer
$15 \div 6 = 2\tfrac{1}{2}$

Answer: $2\frac{1}{2}$ symbols
Why this scores
Mark scheme:
- B1 for $2\frac{1}{2}$ oe
Why this scores full marks: The candidate divides by the key value. Half a symbol represents $3$ cars, so $2$ whole symbols and a half show $12 + 3 = 15$ .
Question 2
Paper 1H/2H style — 1 mark1 mark
A shop wants a bar chart that shows its online sales and its in-store sales for each month, and also makes the total sales for each month easy to read.

Write down whether a composite bar chart or a dual bar chart is better for this, and give a reason. [1]
Model answer
A composite bar chart, because the two kinds of sales are stacked in one bar, so the height of each bar is the total sales for that month.
Why this scores
Mark scheme:
- B1 for composite bar chart with a correct reason, e.g. the height of each bar shows the total oe
Why this scores full marks: The mark needs the choice and the reason. In a dual bar chart the two bars stand side by side, so the total has to be worked out by adding.
Question 3
Paper 1H/2H style — 2 marks2 marks
A pie chart shows how $240$ students travel to school. The sector for walking has an angle of $54^{\circ}$ .

Work out the number of students who walk to school. [2]
Model answer
$\frac{54}{360} \times 240 = 36$

Answer: $36$
Why this scores
Mark scheme:
- M1 for $\frac{54}{360} \times 240$ oe
- A1 for $36$ cao
Why this scores full marks: The sector is $\frac{54}{360}$ of the circle, so it represents the same fraction of the $240$ students. Check: $36$ students at $1.5^{\circ}$ each is $54^{\circ}$ .
Question 4
Paper 1H/2H style — 2 marks2 marks
Maria wants to draw a pictogram to show the numbers $20$ , $35$ , $15$ and $30$ . She will use only whole symbols and half symbols, and she wants no more than $4$ symbols in any row.

(a) Write down the number that one symbol should represent. [1]

(b) Write down the number of symbols Maria should draw for $35$ . [1]
Model answer
(a) Each number must be a whole number of half symbols, so half a symbol must divide $20$ , $35$ , $15$ and $30$ : half a symbol is $5$ (or $1$ ). With $1$ symbol $= 2$ , $35$ would need $17\frac{1}{2}$ symbols, which is too many.

Answer: $10$

(b) $35 \div 10 = 3\tfrac{1}{2}$

Answer: $3\frac{1}{2}$ symbols
Why this scores
Mark scheme:
- B1 for $10$
- B1 for $3\frac{1}{2}$ (ft their key)
Why this scores full marks: The candidate uses both conditions. Half symbols only means half a symbol must divide every number, and at most $4$ symbols means one symbol must be at least $35 \div 4 = 8.75$ . Only $10$ does both.
Question 5
Paper 1H/2H style — 3 marks3 marks
A pie chart has four sectors labelled $35\%$ , $20\%$ , $30\%$ and $15\%$ .

(a) Work out the angle of the $35\%$ sector. [1]

The $20\%$ sector represents $36$ people.

(b) Work out the total number of people represented by the pie chart. [2]
Model answer
(a) $0.35 \times 360 = 126$

Answer: $126^{\circ}$

(b) $20\%$ is $36$ people, so $100\% = 36 \div 0.2 = 180$

Answer: $180$
Why this scores
Mark scheme:
- B1 for $126$
- M1 for $36 \div 0.2$ or $36 \times 5$ oe
- A1 for $180$ cao
Why this scores full marks: In (a) the percentage is used as a fraction of $360^{\circ}$ . In (b) the candidate divides by $0.2$ — the answer must be bigger than $36$ — rather than finding $20\%$ of $36$ .
Question 6
Paper 1H/2H style — 3 marks3 marks
A percentage composite bar chart shows how students travel to two schools. Each bar is $100\%$ tall.

In the bar for School A, the section for walking is $40\%$ . School A has $600$ students.

In the bar for School B, the section for walking is $30\%$ . School B has $900$ students.

Which school has more students who walk? You must show your working. [3]
Model answer
School A: $0.4 \times 600 = 240$

School B: $0.3 \times 900 = 270$

$270 > 240$ , so School B has more students who walk.
Why this scores
Mark scheme:
- M1 for $0.4 \times 600$ or $0.3 \times 900$
- M1 for both $240$ and $270$
- A1 for School B from correct figures
Why this scores full marks: A percentage bar chart shows proportions, so the candidate multiplies each percentage by its own school's total before comparing. Choosing School A from the taller walking section alone scores nothing.
Question 7
Paper 1H/2H style — 3 marks3 marks
Omar is going to record the number of text messages that each of $30$ people sent yesterday. He draws a frequency table with the classes $0$ – $5$ , $5$ – $10$ and $10$ – $15$ .

(a) Give two different reasons why his classes are not suitable. [2]

(b) Write down a suitable set of classes for his table. [1]
Model answer
(a) 1. The classes overlap: $5$ and $10$ are each in two classes, so it is not clear where to put them.

There is no class for more than $15$ messages, so a person who sent, for example, $18$ messages could not be recorded.

(b) $0$ – $4$ , $5$ – $9$ , $10$ – $14$ , $15$ or more
Why this scores
Mark scheme:
- B1 for overlapping classes, e.g. $5$ is in two classes oe
- B1 for no class for values above $15$ oe
- B1 for non-overlapping classes that cover all possible values, including an open class such as " $15$ or more"
Why this scores full marks: Each reason names the problem and gives an example value. The new classes in (b) fix both problems: whole numbers, no overlaps and an open top class.
Question 8
Paper 1H/2H style — 4 marks4 marks
In a pictogram about the books in a classroom, one symbol represents $8$ books.

Fiction: $4\frac{1}{2}$ symbols; Non-fiction: $3$ symbols; Comics: $1\frac{1}{2}$ symbols; Magazines: $1$ symbol

The same information is to be shown in a pie chart.

Work out the angle of each sector. [4]
Model answer
Numbers of books: $4.5 \times 8 = 36, \quad 3 \times 8 = 24, \quad 1.5 \times 8 = 12, \quad 1 \times 8 = 8$

Total $= 80$ , so each book is $360 \div 80 = 4.5^{\circ}$

Fiction $36 \times 4.5 = 162^{\circ}$ ; Non-fiction $24 \times 4.5 = 108^{\circ}$ ; Comics $12 \times 4.5 = 54^{\circ}$ ; Magazines $8 \times 4.5 = 36^{\circ}$

Check: $162 + 108 + 54 + 36 = 360$
Why this scores
Mark scheme:
- M1 for $36$ , $24$ , $12$ and $8$ books, or a total of $80$ books, or a total of $10$ symbols
- M1 for $360 \div 80$ ( $= 4.5$ ) or $360 \div 10$ ( $= 36$ ) oe
- A1 for two correct angles
- A1 for all four angles correct
Why this scores full marks: The candidate converts symbols to books first and checks that the four angles add up to $360^{\circ}$ . Working with symbols instead ( $10$ symbols, so $36^{\circ}$ per symbol) is equally valid and scores full marks, because every symbol represents the same number of books: $4\frac{1}{2} \times 36 = 162^{\circ}$ .
Question 9
Paper 1H/2H style — 4 marks4 marks
Last year $120$ people took part in a survey. In a pie chart of the results, the sector for option A had an angle of $84^{\circ}$ .

This year $150$ people took part. The number who chose option A was $50\%$ more than last year.

Work out the angle of the sector for option A in this year's pie chart. [4]
Model answer
Last year: $\frac{84}{360} \times 120 = 28$

This year: $28 \times 1.5 = 42$

$\frac{42}{150} \times 360 = 100.8$

Answer: $100.8^{\circ}$
Why this scores
Mark scheme:
- M1 for $\frac{84}{360} \times 120$ ( $= 28$ ) oe
- M1 for $28 \times 1.5$ ( $= 42$ ) oe
- M1 for $\frac{42}{150} \times 360$ oe
- A1 for $100.8$ cao
Why this scores full marks: The $50\%$ increase applies to the number of people, not the angle. Increasing $84^{\circ}$ by $50\%$ gives $126^{\circ}$ , which ignores the new total of $150$ . The answer is exact, so it is given in full, not rounded.
Question 10
Paper 1H/2H style — 5 marks5 marks
There are $160$ people at a concert. Each person is an adult or a child, and has a seated ticket or a standing ticket.

The ratio of adults to children is $5 : 3$

$\frac{1}{4}$ of the adults have seated tickets.

The number of children with standing tickets is $5$ times the number of children with seated tickets.

Work out the percentage of the people with seated tickets who are children. Give your answer correct to $1$ decimal place. [5]
Model answer
Adults: $\frac{5}{8} \times 160 = 100, \qquad \text{children} = 60$

Adults with seated tickets: $\frac{1}{4} \times 100 = 25$

Children: seated $k$ , standing $5k$ , so $6k = 60, \quad k = 10$

People with seated tickets: $25 + 10 = 35$

$\frac{10}{35} \times 100 = 28.57\ldots$

Answer: $28.6\%$
Why this scores
Mark scheme:
- M1 for $100$ adults or $60$ children
- M1 for $25$ adults with seated tickets
- M1 for $60 \div 6$ ( $= 10$ ) oe
- M1 for $\frac{10}{35} \times 100$ oe
- A1 for $28.6$ (awrt)
Why this scores full marks: " $5$ times" splits the children into $6$ equal parts, not $5$ . The candidate uses the seated total, $35$ , as the denominator — not $160$ or $60$ — because the question asks for a percentage of the people with seated tickets.

4MA1 Statistical Charts and Diagrams

At a glance

What you’ll learn

Bar charts and pie charts

Frequency polygons

Scatter graphs and correlation

Stem-and-leaf diagrams

Quick recap

Memorise this

How it’s examined

Worked ExamplesStep-by-step solutions to past-paper-style questions

1Build a pie chart

2Scatter graph: correlation

3Line of best fit and prediction

4Frequency polygon

5Stem-and-leaf median

6Why a pie chart's percentages cannot be right [1 mark]

7Putting boundary values into grouped classes [2 marks]

8Comparing proportions from a dual bar chart [3 marks]

9From a bar chart with a missing bar to pie chart angles [4 marks]

10Frequencies in algebra, and one known sector [5 marks]

Model AnswersFull mark-scheme-style answers

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10