Loading…
Loading…
Complete IGCSE Edexcel guide to constructing and interpreting charts and graphs for statistical data. Worked examples for grades 5-8.
IGCSE Edexcel Maths tests bar charts, pie charts, pictograms, frequency polygons, cumulative frequency curves, and histograms (with equal and unequal class widths). You must be able to both construct and interpret each type. Higher-tier questions focus on histograms using frequency density and reading median/quartile values from cumulative frequency curves.
Source: Edexcel IGCSE Mathematics (9-1) Specification 4MA1
Bar charts display categorical or discrete data using bars of equal width. The height of each bar shows the frequency. Bars should have equal gaps between them. Dual bar charts compare two data sets side by side.
Pie charts show proportions of a whole. Each sector angle is calculated as (frequency divided by total) multiplied by 360 degrees. To read a pie chart, measure the angle with a protractor and reverse the calculation to find the frequency.
Pictograms use symbols to represent data where each symbol represents a fixed number of items. Partial symbols represent fractions of that number. Always include a key.
A frequency polygon is drawn by plotting the midpoint of each class interval against its frequency, then joining the points with straight lines. The midpoint is the average of the lower and upper class boundaries.
Frequency polygons are useful for comparing two distributions on the same axes. They give a clearer shape of the distribution than a bar chart and are often used alongside histograms.
A cumulative frequency table shows the running total of frequencies up to each class boundary. To draw the curve, plot each cumulative frequency value against the upper class boundary of its interval. Join the points with a smooth S-shaped curve (ogive).
From a cumulative frequency curve, you can estimate the median (read across from half the total frequency), the lower quartile (quarter of total frequency), and the upper quartile (three-quarters of total frequency). The interquartile range is UQ minus LQ.
When class widths are equal, a histogram looks like a bar chart with no gaps. When class widths are unequal, the y-axis must show frequency density, not frequency.
Frequency density = frequency / class width
Area of bar = frequency density x class width = frequency
To find the frequency from a histogram, calculate the area of the bar (height multiplied by width). To draw a histogram, divide each frequency by its class width to get the height.
A pie chart shows how 60 students travel to school. The sector for "bus" has an angle of 120 degrees. How many students travel by bus?
Step 1: Fraction of the total = 120 / 360 = 1/3
Step 2: Number of students = (1/3) x 60 = 20
Answer: 20 students travel by bus
The cumulative frequency for a data set of 80 values reaches 80 at the top of the curve. Estimate the median and interquartile range from the cumulative frequency curve.
Step 1: Median position = 80 / 2 = 40th value. Read across from 40 on the y-axis to the curve, then down to the x-axis. Suppose this gives 52.
Step 2: Lower quartile position = 80 / 4 = 20th value. Read across from 20: suppose this gives 45.
Step 3: Upper quartile position = 3 x 80 / 4 = 60th value. Read across from 60: suppose this gives 61.
Step 4: IQR = UQ - LQ = 61 - 45 = 16.
Answer: Median = 52, IQR = 16 (values depend on your graph reading)
A histogram has bars for the classes 0-10, 10-20, 20-25, and 25-40. The frequency densities are 1.5, 2, 4, and 1.2 respectively. Find the frequency for each class.
Step 1: Frequency = frequency density x class width
Step 2: Class 0-10: width = 10, frequency = 1.5 x 10 = 15
Step 3: Class 10-20: width = 10, frequency = 2 x 10 = 20
Step 4: Class 20-25: width = 5, frequency = 4 x 5 = 20
Step 5: Class 25-40: width = 15, frequency = 1.2 x 15 = 18
Answer: Frequencies are 15, 20, 20, and 18 (total = 73)
Using frequency instead of frequency density: When class widths are unequal, the y-axis must show frequency density. Plotting raw frequency gives bars with incorrect heights.
Plotting cumulative frequency at the midpoint: Cumulative frequency values must be plotted at the upper class boundary, not the midpoint. Plotting at the midpoint shifts the entire curve.
Leaving gaps in histograms: Histograms show continuous data so bars must touch. Leaving gaps (as in a bar chart) loses marks.
Misreading scales on given charts: Always check the scale on both axes before reading values. A common error is assuming each square represents 1 unit when it actually represents 2 or 5.
Label all axes: Always include axis labels and a title. Missing labels can cost marks even if the graph itself is correct.
Use a ruler and sharp pencil: Neat, accurate graphs earn full marks. Wobbly lines and imprecise plotting lose marks for accuracy.
Check your cumulative frequency totals: The final cumulative frequency value should equal the total frequency given in the question. If it does not match, there is an error in your running totals.
Draw construction lines on cumulative frequency graphs: Use a ruler to draw horizontal lines from the y-axis to the curve and vertical lines down to the x-axis. These construction lines show the examiner your method and earn marks even if the reading is slightly off.
Statistics & Probability Hub
All topics in this area
Statistical Measures — Mean, Median, Mode
Next topic in this area
Worksheets & Answers
Free practice for statistics topics
IGCSE Tutors in Dubai
Specialist in-home IGCSE support
Maths Tutors in Dubai
Expert maths tutoring at home
Contact GetYourTutors — IGCSE Maths Data Representation
Phone: (+971) 4-313-2715 | Mobile: 050-947-9432
WhatsApp: 050-947-9432
Email: info@getyourtutors.com
Emirates Towers, Office Tower, Level 41, Sheikh Zayed Road, PO Box 31003, Dubai, UAE
Last updated: March 2026
Everything you need to know about our private tutoring services in Dubai.
A dedicated tutor builds confident graph-drawing and data-reading skills for every chart type. In-home across Dubai.