9.2

Averages and measures of spread

Cambridge IGCSE Mathematics (0580)  · Unit 9: Statistics  · 10 flashcards

Averages and measures of spread is topic 9.2 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 9 — Statistics , alongside Data collection and display, Cumulative frequency and box plots and Correlation and scatter diagrams.  In one line: The 'mean' is the average of a set of numbers. It's calculated by summing all the values and dividing by the total number of values.

This topic is examined across Paper 1 (Core) or Paper 2 (Extended) — non-calculator — and Paper 3 (Core) or Paper 4 (Extended) — calculator.

The deck below contains 10 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.

Key definition

'mean' and explain how it's calculated

The 'mean' is the average of a set of numbers. It's calculated by summing all the values and dividing by the total number of values.

Example: Mean of 2, 4, 6 is (2+4+6)/3 = 4.

Questions this Averages and measures of spread deck will help you answer

Definition Flip

Define 'mean' and explain how it's calculated.

Answer Flip

The 'mean' is the average of a set of numbers. It's calculated by summing all the values and dividing by the total number of values.

Example: Mean of 2, 4, 6 is (2+4+6)/3 = 4.
Key Concept Flip

Explain the difference between 'mean', 'median' and 'mode'.

Answer Flip

Mean is the average, median is the middle value when data is ordered, and mode is the most frequent value.

Example: For 2, 3, 3, 4, 5, mean=3.4, median=3, mode=3.
Definition Flip

What is the 'range' and how is it calculated?

Answer Flip

The 'range' is a measure of spread indicating the difference between the highest and lowest values in a dataset. It's calculated by subtracting the lowest value from the highest value.

Example: For 2, 4, 6, 8, range = 8 - 2 = 6.
Key Concept Flip

How do you find the median from a frequency table?

Answer Flip

Locate the middle value based on the cumulative frequency. If there are 'n' data points, find the (n+1)/2 th value. Consider the intervals of the frequency table to find the data point corresponding to that cumulative frequency.

Key Concept Flip

Describe how to calculate an 'estimated mean' from grouped data.

Answer Flip

Multiply the midpoint of each class interval by its frequency, sum these products, and then divide by the total frequency. This gives an approximation of the mean when individual data points are unavailable.

Definition Flip

Define 'modal class' in the context of grouped data.

Answer Flip

The 'modal class' is the class interval with the highest frequency in a grouped data set. It represents the most common range of values within the data.

Example: If the class 10-20 has highest frequency, it's the modal class.
Definition Flip

What is the 'interquartile range' (IQR) and how is it calculated?

Answer Flip

The IQR is a measure of statistical dispersion, representing the difference between the upper quartile (Q3) and the lower quartile (Q1). IQR = Q3 - Q1. It shows the spread of the middle 50% of the data.

Key Concept Flip

Explain how to find the lower quartile (Q1) and upper quartile (Q3) of a data set.

Answer Flip

Q1 is the median of the lower half of the data, and Q3 is the median of the upper half. Ensure the data is ordered first. If 'n' is the number of values: Q1 position ≈ (n+1)/4 and Q3 position ≈ 3(n+1)/4.

Key Concept Flip

How can the IQR be used to identify outliers in a dataset?

Answer Flip

Outliers can be identified using the 1.5 x IQR rule. Values below Q1 - 1.5 x IQR or above Q3 + 1.5 x IQR are considered outliers, indicating values significantly different from the rest of the data.

Key Concept Flip

When would the median be a better measure of central tendency than the mean?

Answer Flip

The median is preferred when the data contains outliers or is skewed, as the mean is sensitive to extreme values. The median provides a more robust measure of the 'typical' value in these cases.

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9.1 Data collection and display 9.3 Cumulative frequency and box plots

Key Questions: Averages and measures of spread

Define 'mean' and explain how it's calculated.

The 'mean' is the average of a set of numbers. It's calculated by summing all the values and dividing by the total number of values.

Example: Mean of 2, 4, 6 is (2+4+6)/3 = 4.
What is the 'range' and how is it calculated?

The 'range' is a measure of spread indicating the difference between the highest and lowest values in a dataset. It's calculated by subtracting the lowest value from the highest value.

Example: For 2, 4, 6, 8, range = 8 - 2 = 6.
Define 'modal class' in the context of grouped data.

The 'modal class' is the class interval with the highest frequency in a grouped data set. It represents the most common range of values within the data.

Example: If the class 10-20 has highest frequency, it's the modal class.
What is the 'interquartile range' (IQR) and how is it calculated?

The IQR is a measure of statistical dispersion, representing the difference between the upper quartile (Q3) and the lower quartile (Q1). IQR = Q3 - Q1. It shows the spread of the middle 50% of the data.

More topics in Unit 9 — Statistics

Averages and measures of spread sits alongside these Mathematics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.

9.1 Data collection and display

10 flashcards
9.3 Cumulative frequency and box plots

10 flashcards
9.4 Correlation and scatter diagrams

9 flashcards
9.5 Histograms

9 flashcards

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.

mean median mode range average measure of central tendency frequency table grouped data modal class estimated mean interquartile range IQR quartile lower quartile upper quartile

Key terms covered in this Averages and measures of spread 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.

'mean' and explain how it's calculated
The 'range' and how is it calculated
'modal class' in the context of grouped data
The 'interquartile range' (IQR) and how is it calculated

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