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31 Dec 2025

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5 pages

Mastering GCSE Maths: Learn Cumulative Frequency Graphs

ThomasK

@ttomkirb_314

Ever wondered how to find the middle value in a... Show more

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2 The cumulative frequency graph gives some information the times it took people to complete a challenge

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Reading Cumulative Frequency Graphs

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.

Creating Cumulative Frequency Tables

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.

Plotting Cumulative Frequency Graphs

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.

Advanced Applications and Estimations

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 $like 90 km/h$ , 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.

Finding Medians and Statistical Measures

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.

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295

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31 Dec 2025

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5 pages

Mastering GCSE Maths: Learn Cumulative Frequency Graphs

ThomasK

@ttomkirb_314

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.