Cumulative frequency and box plots
Cambridge IGCSE Mathematics (0580) · Unit 9: Statistics · 10 flashcards
Cumulative frequency and box plots is topic 9.3 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 9 — Statistics , alongside Data collection and display, Averages and measures of spread and Correlation and scatter diagrams. In one line: Cumulative frequency is the running total of frequencies. It's calculated by adding the frequency of the current class to the cumulative frequency of the previous class.
This topic is examined across Paper 1 (Core) or Paper 2 (Extended) — non-calculator — and Paper 3 (Core) or Paper 4 (Extended) — calculator. It is a Supplement (Extended-tier) topic, so it appears only on the Extended-tier papers.
The deck below contains 10 flashcards — 6 definitions, 2 key concepts and 1 application card — covering the precise wording mark schemes reward. Use the 6 definition cards to lock down command-word answers (define, state), then move on to the concept and application cards to handle explain, describe and compare questions.
Cumulative frequency. How is it calculated
Cumulative frequency is the running total of frequencies. It's calculated by adding the frequency of the current class to the cumulative frequency of the previous class.
Questions this Cumulative frequency and box plots deck will help you answer
- › Explain how to estimate the median from a cumulative frequency diagram.
- › Explain how to construct a box plot (box and whisker plot).
- › How can box plots be used to compare two or more sets of data?
Define cumulative frequency. How is it calculated?
Cumulative frequency is the running total of frequencies. It's calculated by adding the frequency of the current class to the cumulative frequency of the previous class.
What is an ogive (cumulative frequency curve)?
An ogive is a line graph of cumulative frequency data plotted against the upper class boundaries. It's used to estimate the median, quartiles, and percentiles from grouped data. The x-axis shows the upper bound of each class and the y-axis the cumulative frequency.
Explain how to estimate the median from a cumulative frequency diagram.
The median is the middle value of the data. On a cumulative frequency diagram, find half the total frequency on the y-axis, then read across to the curve and down to the x-axis to find the corresponding value, which is the estimated median.
Define the lower quartile (Q1) and the upper quartile (Q3).
The lower quartile (Q1) is the value that separates the bottom 25% of the data. The upper quartile (Q3) is the value that separates the top 25% of the data. Q1 corresponds to the 25th percentile, and Q3 to the 75th percentile.
How do you find the interquartile range (IQR)? What does it represent?
The interquartile range (IQR) is the difference between the upper and lower quartiles: IQR = Q3 - Q1. It represents the spread of the middle 50% of the data. A smaller IQR indicates less variability in the central data.
Describe the five-number summary used to create a box plot.
The five-number summary consists of the minimum value, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum value. These five values are used to construct the box plot, visually representing the distribution of the data.
Explain how to construct a box plot (box and whisker plot).
Draw a number line covering the range of the data. Draw a box from Q1 to Q3 with a line indicating the median. Draw whiskers extending from the box to the minimum and maximum values (unless outliers are present).
What is an outlier, and how can it be identified using the IQR?
An outlier is a data point that is significantly different from other data points. A common rule is to consider values less than Q1 - 1.5*IQR or greater than Q3 + 1.5*IQR as outliers.
A set of data has Q1 = 20 and Q3 = 50. Calculate the upper and lower outlier boundaries.
IQR = 50 - 20 = 30. Lower boundary = 20 - (1.5 * 30) = -25. Upper boundary = 50 + (1.5 * 30) = 95. Any values below -25 or above 95 would be considered outliers.
How can box plots be used to compare two or more sets of data?
By comparing the medians, IQRs, and ranges of the box plots, you can assess the central tendency, spread, and skewness of the different datasets. Overlapping boxes indicate similar central 50% ranges, while differing whisker lengths indicate different overall ranges.
Key Questions: Cumulative frequency and box plots
Define cumulative frequency. How is it calculated?
Cumulative frequency is the running total of frequencies. It's calculated by adding the frequency of the current class to the cumulative frequency of the previous class.
What is an ogive (cumulative frequency curve)?
An ogive is a line graph of cumulative frequency data plotted against the upper class boundaries. It's used to estimate the median, quartiles, and percentiles from grouped data. The x-axis shows the upper bound of each class and the y-axis the cumulative frequency.
Define the lower quartile (Q1) and the upper quartile (Q3).
The lower quartile (Q1) is the value that separates the bottom 25% of the data. The upper quartile (Q3) is the value that separates the top 25% of the data. Q1 corresponds to the 25th percentile, and Q3 to the 75th percentile.
How do you find the interquartile range (IQR)? What does it represent?
The interquartile range (IQR) is the difference between the upper and lower quartiles: IQR = Q3 - Q1. It represents the spread of the middle 50% of the data. A smaller IQR indicates less variability in the central data.
Describe the five-number summary used to create a box plot.
The five-number summary consists of the minimum value, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum value. These five values are used to construct the box plot, visually representing the distribution of the data.
More topics in Unit 9 — Statistics
Cumulative frequency and box plots sits alongside these Mathematics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.
Cambridge syllabus keywords to use in your answers
These are the official Cambridge 0580 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.
Key terms covered in this Cumulative frequency and box plots deck
Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.
Related Mathematics guides
Long-read articles that go beyond the deck — cover the whole subject's common mistakes, high-yield content and revision pacing.
How to study this Cumulative frequency and box plots deck
Start in Study Mode, attempt each card before flipping, then rate Hard, Okay or Easy. Cards you rate Hard come back within a day; cards you rate Easy push out to weeks. Your progress is saved in your browser, so come back daily for 5–10 minute reviews until every card reads Mastered.
Study Mode
Space to flip • ←→ to navigate • Esc to close
You're on a roll!
You've viewed 10 topics today
Create a free account to unlock unlimited access to all revision notes, flashcards, and study materials.
You're all set!
Enjoy unlimited access to all study materials.
Something went wrong. Please try again.
What you'll get:
- Unlimited revision notes & flashcards
- Track your study progress
- No spam, just study updates