Histograms
Cambridge IGCSE Mathematics (0580) · Unit 9: Statistics · 9 flashcards
Histograms is topic 9.5 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 9 — Statistics , alongside Data collection and display, Averages and measures of spread and Cumulative frequency and box plots. In one line: A histogram represents continuous data with bars whose *area* is proportional to the frequency. Unlike bar charts (discrete data), the *width* of the bars in a histogram can vary, requiring the use of frequency density.
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 9 flashcards — 4 definitions, 1 key concept and 2 application cards — covering the precise wording mark schemes reward. Use the 4 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.
A histogram, and how does it differ from a bar chart
A histogram represents continuous data with bars whose *area* is proportional to the frequency. Unlike bar charts (discrete data), the *width* of the bars in a histogram can vary, requiring the use of frequency density.
Questions this Histograms deck will help you answer
- › A histogram shows the ages of people in a club. The bar representing ages 20-30 has a height (frequency density) of 2.5. What does this tell you?
- › In a histogram with unequal class intervals, why is it crucial to use frequency density rather than just frequency for the bar heights?
- › Describe how you would draw a histogram given a frequency table with unequal class intervals.
What is a histogram, and how does it differ from a bar chart?
A histogram represents continuous data with bars whose *area* is proportional to the frequency. Unlike bar charts (discrete data), the *width* of the bars in a histogram can vary, requiring the use of frequency density.
Define 'frequency density' in the context of histograms.
Frequency density is a measure of how many data points fall within a specific class interval, calculated as: Frequency Density = Frequency / Class Width. It's used when class intervals are unequal.
How do you calculate the frequency density for a class with a frequency of 20 and a class width of 5?
Frequency density = Frequency / Class Width = 20 / 5 = 4. The frequency density for that class is 4.
If the area of a bar in a histogram is 30 cm² and the class width is 6 cm, what is the frequency?
Area = Frequency Density x Class Width, and Frequency = Frequency Density x Class Width = Area. Therefore, Frequency = 30 cm².
Explain how to determine the class width from a histogram.
The class width is the difference between the upper and lower boundaries of a class interval. On a histogram, it's the width of the bar corresponding to that class.
A histogram shows the ages of people in a club. The bar representing ages 20-30 has a height (frequency density) of 2.5. What does this tell you?
This means that the frequency density for the 20-30 age group is 2.5. If the scale represents that 1cm=1 person, 2.5 shows how many people fit into that portion of the ages.
In a histogram with unequal class intervals, why is it crucial to use frequency density rather than just frequency for the bar heights?
Using frequency directly would misrepresent the data because wider class intervals would appear to have disproportionately high frequencies. Frequency density corrects for this by considering the width of the interval.
Describe how you would draw a histogram given a frequency table with unequal class intervals.
First, calculate the frequency density for each class interval (Frequency/Class Width). Then, draw the histogram with the x-axis representing the continuous variable and the y-axis representing the frequency density. The area of each bar represents the frequency of that class.
Explain how histograms are useful for representing 'continuous data'. Give an example of continuous data.
Histograms are ideal for showing the distribution of continuous data, which can take any value within a range.
Key Questions: Histograms
What is a histogram, and how does it differ from a bar chart?
A histogram represents continuous data with bars whose *area* is proportional to the frequency. Unlike bar charts (discrete data), the *width* of the bars in a histogram can vary, requiring the use of frequency density.
Define 'frequency density' in the context of histograms.
Frequency density is a measure of how many data points fall within a specific class interval, calculated as: Frequency Density = Frequency / Class Width. It's used when class intervals are unequal.
Explain how to determine the class width from a histogram.
The class width is the difference between the upper and lower boundaries of a class interval. On a histogram, it's the width of the bar corresponding to that class.
Explain how histograms are useful for representing 'continuous data'. Give an example of continuous data.
Histograms are ideal for showing the distribution of continuous data, which can take any value within a range.
More topics in Unit 9 — Statistics
Histograms 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 Histograms 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.
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