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Maths
8 Dec 2025
294
5 pages
ThomasK @ttomkirb_314
Ever wondered how to find the middle value in a large dataset or work out how many people... Show more
Reading cumulative frequency graphs is like being a data detective – you're hunting for specific values that tell a story about your dataset. The median is always found at the halfway point of your total frequency.
To find the median, you'll need to locate 50% of your total data points on the y-axis, then read across to your curve and down to find the corresponding value. In this challenge completion example, with the median at 68 seconds, half the people finished faster and half took longer.
Finding how many people exceed a certain value is equally straightforward. You simply read the cumulative frequency at your target value (80 seconds here) and subtract this from the total to get your answer.
Quick Tip Always remember that cumulative frequency shows "up to and including" that value, so think carefully about whether you want "more than" or "at least" when interpreting your results.
Building a cumulative frequency table from a regular frequency table is like climbing stairs – each step adds to what you've already climbed. You're essentially creating a running total that shows how many items fall within each boundary.
The process is surprisingly simple start with your first frequency value, then keep adding each subsequent frequency to your running total. For the cat weights example, you go from 8, to 8+10=18, to 18+21=39, and so on until you reach your final total of 80 cats.
Cumulative frequency graphs are plotted using the upper boundary of each class interval on the x-axis. The points are then connected with smooth curves, creating your visual tool for reading off quartiles and other statistical measures.
Remember The interquartile range is found by subtracting Q1 (25% position) from Q3 (75% position), giving you a measure of how spread out the middle 50% of your data is.
Drawing cumulative frequency graphs transforms your numerical data into a powerful visual tool that makes complex calculations much simpler. The key is plotting each point at the upper class boundary with its corresponding cumulative frequency value.
Your graph should show a smooth, increasing curve that never goes down – after all, you're always adding more data as you move right along the x-axis. Each point represents the total number of items up to that particular boundary value.
The beauty of these graphs lies in their versatility for reading off statistical measures. Once plotted correctly, you can find quartiles, estimate medians, and determine how many items fall above or below any given value.
Pro Tip Always double-check that your final plotted point matches your total frequency – if it doesn't, you've made an error somewhere in your cumulative frequency calculations.
Cumulative frequency graphs become incredibly useful when you need to estimate values that fall between your plotted points. Reading from the graph allows you to interpolate and find approximate answers for any value within your data range.
When estimating how many cars travel over a specific speed , you read the cumulative frequency at that point and subtract from your total. This technique works because the cumulative frequency tells you how many cars travel up to that speed.
The smooth curve you draw between points assumes an even distribution within each class interval. While this isn't always perfectly accurate, it provides excellent estimates that are more than sufficient for most practical purposes.
Key Insight These estimation techniques are particularly valuable in real-world scenarios where you need quick approximations without access to the raw individual data points.
The median is your most reliable measure of central tendency when dealing with grouped data, and cumulative frequency graphs make finding it remarkably straightforward. Simply locate 50% of your total frequency on the y-axis and read across to find your answer.
For 100 people with a median travel time of 52.3 minutes, you know that exactly half took longer and half took less time than this value. This gives you immediate insight into your data's central tendency without needing complex calculations.
Statistical measures like quartiles follow the same principle – Q1 at 25%, median at 50%, and Q3 at 75% of your total frequency. These values help you understand not just the centre of your data, but how it's distributed across the entire range.
Final Tip Practice reading these graphs accurately by always starting from the y-axis value, moving horizontally to the curve, then vertically down to read your answer – this systematic approach prevents reading errors.
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
3
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore the fundamentals of histograms and frequency tables, essential for iGCSE Maths. This resource covers key concepts such as cumulative frequency, frequency density, and step-by-step instructions for drawing histograms and cumulative frequency graphs. Ideal for students preparing for exams.
MathsComprehensive study material covering essential GCSE statistics topics including normal distribution, measures of central tendency, probability models, and data visualization techniques. Ideal for Edexcel Paper 2 revision, this resource includes detailed explanations of box plots, histograms, and the 68-95-99.7 rule, ensuring a solid understanding for achieving top grades.
MathsExplore key concepts from the OCR GCSE Higher Tier Mathematics Paper 5 (Non-Calculator). This study resource covers essential topics such as trigonometric values, probability, area calculations, and geometric constructions. Perfect for exam preparation, it includes practice questions on median, cumulative frequency, and graphing inequalities. Enhance your understanding and boost your confidence for the exam!
MathsExplore the fundamentals of histograms, including their structure, frequency density calculations, and practical examples. This summary covers key concepts such as continuous data representation, bar spacing, and how to interpret histograms through provided tables and graphs. Ideal for exam preparation and enhancing your understanding of data visualization.
MathsExplore the fundamentals of geometric transformations including translations, reflections, rotations, and enlargements. This summary covers key concepts such as translation vectors, reflection lines, rotation directions, and scale factors, providing clear examples and explanations for each transformation type.
MathsExplore essential data analysis techniques including two-way tables, box plots, correlation, and various data representations. This summary covers key concepts such as measures of location, statistical averages, and graphical representations like bar charts and pie charts. Ideal for Year 7 students looking to enhance their understanding of data in mathematics.
MathsApp Store
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
ThomasK
@ttomkirb_314
Ever wondered how to find the middle value in a large dataset or work out how many people fall above a certain threshold? Cumulative frequency graphs are your secret weapon for analysing grouped data and answering these exact questions quickly... Show more
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Reading cumulative frequency graphs is like being a data detective – you're hunting for specific values that tell a story about your dataset. The median is always found at the halfway point of your total frequency.
To find the median, you'll need to locate 50% of your total data points on the y-axis, then read across to your curve and down to find the corresponding value. In this challenge completion example, with the median at 68 seconds, half the people finished faster and half took longer.
Finding how many people exceed a certain value is equally straightforward. You simply read the cumulative frequency at your target value (80 seconds here) and subtract this from the total to get your answer.
Quick Tip: Always remember that cumulative frequency shows "up to and including" that value, so think carefully about whether you want "more than" or "at least" when interpreting your results.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Building a cumulative frequency table from a regular frequency table is like climbing stairs – each step adds to what you've already climbed. You're essentially creating a running total that shows how many items fall within each boundary.
The process is surprisingly simple: start with your first frequency value, then keep adding each subsequent frequency to your running total. For the cat weights example, you go from 8, to 8+10=18, to 18+21=39, and so on until you reach your final total of 80 cats.
Cumulative frequency graphs are plotted using the upper boundary of each class interval on the x-axis. The points are then connected with smooth curves, creating your visual tool for reading off quartiles and other statistical measures.
Remember: The interquartile range is found by subtracting Q1 (25% position) from Q3 (75% position), giving you a measure of how spread out the middle 50% of your data is.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Drawing cumulative frequency graphs transforms your numerical data into a powerful visual tool that makes complex calculations much simpler. The key is plotting each point at the upper class boundary with its corresponding cumulative frequency value.
Your graph should show a smooth, increasing curve that never goes down – after all, you're always adding more data as you move right along the x-axis. Each point represents the total number of items up to that particular boundary value.
The beauty of these graphs lies in their versatility for reading off statistical measures. Once plotted correctly, you can find quartiles, estimate medians, and determine how many items fall above or below any given value.
Pro Tip: Always double-check that your final plotted point matches your total frequency – if it doesn't, you've made an error somewhere in your cumulative frequency calculations.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Cumulative frequency graphs become incredibly useful when you need to estimate values that fall between your plotted points. Reading from the graph allows you to interpolate and find approximate answers for any value within your data range.
When estimating how many cars travel over a specific speed , you read the cumulative frequency at that point and subtract from your total. This technique works because the cumulative frequency tells you how many cars travel up to that speed.
The smooth curve you draw between points assumes an even distribution within each class interval. While this isn't always perfectly accurate, it provides excellent estimates that are more than sufficient for most practical purposes.
Key Insight: These estimation techniques are particularly valuable in real-world scenarios where you need quick approximations without access to the raw individual data points.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
The median is your most reliable measure of central tendency when dealing with grouped data, and cumulative frequency graphs make finding it remarkably straightforward. Simply locate 50% of your total frequency on the y-axis and read across to find your answer.
For 100 people with a median travel time of 52.3 minutes, you know that exactly half took longer and half took less time than this value. This gives you immediate insight into your data's central tendency without needing complex calculations.
Statistical measures like quartiles follow the same principle – Q1 at 25%, median at 50%, and Q3 at 75% of your total frequency. These values help you understand not just the centre of your data, but how it's distributed across the entire range.
Final Tip: Practice reading these graphs accurately by always starting from the y-axis value, moving horizontally to the curve, then vertically down to read your answer – this systematic approach prevents reading errors.
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
3
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore the fundamentals of histograms and frequency tables, essential for iGCSE Maths. This resource covers key concepts such as cumulative frequency, frequency density, and step-by-step instructions for drawing histograms and cumulative frequency graphs. Ideal for students preparing for exams.
MathsComprehensive study material covering essential GCSE statistics topics including normal distribution, measures of central tendency, probability models, and data visualization techniques. Ideal for Edexcel Paper 2 revision, this resource includes detailed explanations of box plots, histograms, and the 68-95-99.7 rule, ensuring a solid understanding for achieving top grades.
MathsExplore key concepts from the OCR GCSE Higher Tier Mathematics Paper 5 (Non-Calculator). This study resource covers essential topics such as trigonometric values, probability, area calculations, and geometric constructions. Perfect for exam preparation, it includes practice questions on median, cumulative frequency, and graphing inequalities. Enhance your understanding and boost your confidence for the exam!
MathsExplore the fundamentals of histograms, including their structure, frequency density calculations, and practical examples. This summary covers key concepts such as continuous data representation, bar spacing, and how to interpret histograms through provided tables and graphs. Ideal for exam preparation and enhancing your understanding of data visualization.
MathsExplore the fundamentals of geometric transformations including translations, reflections, rotations, and enlargements. This summary covers key concepts such as translation vectors, reflection lines, rotation directions, and scale factors, providing clear examples and explanations for each transformation type.
MathsExplore essential data analysis techniques including two-way tables, box plots, correlation, and various data representations. This summary covers key concepts such as measures of location, statistical averages, and graphical representations like bar charts and pie charts. Ideal for Year 7 students looking to enhance their understanding of data in mathematics.
MathsApp Store
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
