Statistical Charts & Scatter Diagrams
MathematicsΒ· 9.4, 9.5Β· 20 min read
1. Interpreting & Drawing Core Statistical Chartsβ β ββββ± 6 min
Core CIE IGCSE 0580 questions require you to read values from, draw, and calculate summary statistics from five common statistical chart types: bar charts, pie charts, pictograms, stem-and-leaf diagrams, and simple frequency tables.
Simple Frequency Distribution
A table that lists each data value or category alongside the number of times it appears in a dataset
Example:
A frequency table for favourite colours might list Red: 8, Blue: 12, Green: 5
Pictograms: Use symbols to represent fixed numbers of data points. Always check the key to find the value of each symbol.
Bar charts: Use rectangular bars of equal width to compare category frequencies. The height of each bar corresponds to frequency.
Pie charts: Use sectors of a circle to show the proportion of each category relative to the total dataset. The angle of each sector is proportional to its frequency.
Stem-and-leaf diagrams: Group numerical data by place value to retain individual data points, making it easy to calculate median, mode and range.
A pictogram shows ice cream sales over 4 days. Key: 1 ice cream symbol = 5 ice creams. Day 1: 3 symbols, Day 2: 2.5 symbols, Day 3: 4 symbols, Day 4: 1.5 symbols. Calculate total ice cream sales over the 4 days.
- 1
Count the total number of symbols across all days: 3 + 2.5 + 4 + 1.5 = 11 symbols
- 2
Multiply the total number of symbols by the value per symbol from the key: 11 Γ 5 = 55
- 3
Final answer: 55 ice creams
Exam tip:
Always show your working for chart calculation questions, even if the question looks simple. You can get method marks even if your final answer is wrong.
2. Scatter Diagrams & Correlationβ β ββββ± 5 min
Scatter diagrams plot pairs of bivariate data (two variables measured on the same sample) on a coordinate grid to show the relationship between the two variables. This relationship is called correlation.
Correlation
A measure of the strength and direction of the linear relationship between two variables on a scatter diagram
Positive correlation: As one variable increases, the other variable also increases (e.g. height and weight in teenagers)
Negative correlation: As one variable increases, the other variable decreases (e.g. hours spent exercising and resting heart rate)
No correlation: There is no clear linear relationship between the two variables (e.g. shoe size and exam score)
Strong correlation: Plotted points lie very close to an invisible straight line
Weak correlation: Plotted points are spread out but still show a clear upward or downward trend
A scatter diagram plots hours spent revising for a maths test against test score. Plotted points form a clear upward trend, with points lying close to a straight line. Describe the correlation shown.
- 1
Identify the direction of the trend: upward trend = positive correlation
- 2
Identify the strength: points lie close to a straight line = strong correlation
- 3
Final description: Strong positive correlation
Exam tip:
If there is no obvious trend, always state 'no correlation' rather than guessing a weak positive or negative trend.
3. Lines of Best Fit & Estimationβ β β βββ± 5 min
If a scatter diagram shows strong or weak positive/negative correlation, you can draw a line of best fit by eye to make estimates for values not plotted on the diagram.
Line of best fit
A straight line drawn through a scatter diagram that passes as close as possible to all plotted points, with roughly equal numbers of points above and below the line
Use a ruler to draw a straight line
Position the line so that an equal number of plotted points lie above and below the line where possible
The line does not need to pass through the origin (0,0) unless the plotted data naturally falls that way
You do not need to pass the line through any specific plotted points
A scatter diagram showing hours spent revising (x-axis, 0 to 10 hours) vs test score (y-axis, 0 to 100 marks) shows strong positive correlation. A student spent 6 hours revising, which is a value within the range of plotted revision times. Explain how to use a line of best fit to estimate their test score.
- 1
Locate 6 hours on the x-axis of the scatter diagram
- 2
Draw a vertical line up from 6 hours until you meet the line of best fit
- 3
Draw a horizontal line left from this intersection point to the y-axis to read the estimated test score
- 4
This is an example of interpolation, which is a reliable estimate since 6 hours is within the range of the original data
Exam tip:
If you are estimating a value outside the range of the plotted data (extrapolation), always note that this estimate may be unreliable, as you cannot assume the relationship continues outside the measured range.
4. Exam Command Terms & Mixed Practiceβ β β βββ± 4 min
A class collects data on the number of minutes each student spends travelling to school and their score on a first lesson maths quiz. a) Name the type of chart that should be used to show the relationship between travel time and quiz score. b) The chart shows a clear downward trend with points spread out but clearly aligned. Describe the correlation. c) Use the line of best fit that passes through (20, 65) to estimate the quiz score for a student who travels 20 minutes to school.
- 1
a) The correct chart type is a scatter diagram, as it shows the relationship between two numerical variables
- 2
b) Downward trend = negative correlation, points spread out but clearly aligned = weak correlation, so overall weak negative correlation
- 3
c) The estimated score is the y-value at x=20 on the line of best fit, which is 65 marks
5. Common Pitfalls
Wrong move:
Forgetting to check the key on a pictogram, counting each symbol as 1 unit
Why:
Pictogram symbols almost always represent more than 1 data point, so missing the key leads to incorrect frequency counts
Correct move:
Always locate and note the pictogram key before attempting any calculations
Wrong move:
Drawing a line of best fit through the origin even when the data does not cluster near (0,0)
Why:
Lines of best fit follow the trend of the data, not the axes. Forcing the line through the origin leads to incorrect estimates
Correct move:
Position the line to follow the plotted trend, with equal numbers of points above and below the line
Wrong move:
Describing correlation even when there is no clear trend in the scatter diagram
Why:
Correlation only applies to linear relationships; stating a correlation when there is none shows lack of understanding
Correct move:
If points are randomly scattered with no upward or downward trend, explicitly state 'no correlation'
Wrong move:
Drawing a curved line of best fit for Core tier questions
Why:
CIE IGCSE 0580 Core only requires straight lines of best fit for linear correlation
Correct move:
Always use a ruler to draw a straight line of best fit for any scatter diagram with linear correlation
Wrong move:
Using the height of a pie chart sector to estimate frequency, instead of using the angle
Why:
Pie chart sectors are proportional by angle, not height or area perception
Correct move:
Calculate the frequency of a pie chart sector using the formula: (sector angle / 360) Γ total frequency
6. Quick Reference Cheatsheet
Chart Type | Key Use Case | Core Calculation Rule |
|---|---|---|
Pictogram | Compare category frequencies with visual symbols | Frequency = number of symbols Γ key value per symbol |
Bar Chart | Compare discrete category frequencies | Frequency = height of bar (check y-axis scale) |
Pie Chart | Show proportion of each category to total | Sector frequency = (sector angle Γ· 360) Γ total sample size |
Stem-and-leaf | Retain individual data points for summary stats | Always order leaves from smallest to largest on each stem |
Scatter Diagram | Show relationship between two numerical variables | Correlation = direction (positive/negative) + strength (strong/weak/none) |
Line of Best Fit | Estimate unknown values from correlated data | Draw with ruler, equal points above/below line |
7. Frequently Asked
Do I need to use a ruler for the line of best fit?
Yes, always use a straight edge (ruler) to draw your line of best fit. The line should pass as close as possible to all plotted points, with roughly equal numbers of points above and below the line.
How do I tell the difference between strong and weak correlation?
For strong correlation, plotted points lie very close to an invisible straight line. For weak correlation, points are more spread out but still show a clear upward or downward trend.
Can I draw a line of best fit if there is no correlation?
No. Lines of best fit only apply to datasets with clear positive or negative linear correlation. Drawing one for uncorrelated data will produce meaningless estimates.
Going deeper
What's Next
Now that you have mastered core statistical charts and scatter diagrams for CIE IGCSE 0580 Core, you are ready to practice past paper questions to reinforce your skills, or move on to learning how to calculate summary statistics including mean, median, mode and range. These skills are also foundational for probability topics later in the syllabus, as well as for AS Level Mathematics if you choose to continue your studies. Make sure to practice drawing lines of best fit and interpreting each chart type under timed conditions to build speed and accuracy for your exam.