9.5

Histograms

9 flashcards to master Histograms

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Definition Flip

What is a histogram, and how does it differ from a bar chart?

Answer Flip

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.

Definition Flip

Define 'frequency density' in the context of histograms.

Answer Flip

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.

Key Concept Flip

How do you calculate the frequency density for a class with a frequency of 20 and a class width of 5?

Answer Flip

Frequency density = Frequency / Class Width = 20 / 5 = 4. The frequency density for that class is 4.

Key Concept Flip

If the area of a bar in a histogram is 30 cm² and the class width is 6 cm, what is the frequency?

Answer Flip

Area = Frequency Density x Class Width, and Frequency = Frequency Density x Class Width = Area. Therefore, Frequency = 30 cm².

Definition Flip

Explain how to determine the class width from a histogram.

Answer Flip

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.

Key Concept Flip

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?

Answer Flip

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.

Key Concept Flip

In a histogram with unequal class intervals, why is it crucial to use frequency density rather than just frequency for the bar heights?

Answer Flip

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.

Key Concept Flip

Describe how you would draw a histogram given a frequency table with unequal class intervals.

Answer Flip

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.

Definition Flip

Explain how histograms are useful for representing 'continuous data'. Give an example of continuous data.

Answer Flip

Histograms are ideal for showing the distribution of continuous data, which can take any value within a range.

Example: height, weight, temperature, or time.

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9.4 Correlation and scatter diagrams

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.

Example: height, weight, temperature, or time.

About Histograms (9.5)

These 9 flashcards cover everything you need to know about Histograms for your Cambridge IGCSE Mathematics (0580) exam. Each card is designed based on the official syllabus requirements.

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