Averages & Range
Master mean, median, mode, and measures of spread—and know which one to use when.
Quick Overview
- Discrete vs Continuous: Discrete data takes specific values (shoes, people). Continuous data takes any value (height, time).
- Mode: The most frequent value. Good for non-numerical data.
- Median: The middle value when ordered. Unaffected by extreme values.
- Mean: Sum ÷ number of values. Most common but sensitive to outliers.
- Range: Highest − lowest. Simple but affected by extremes.
- Interquartile Range: Upper quartile − lower quartile. Better for comparing spreads.
- Frequency Tables: Organise data; use midpoints for grouped data.
- Comparing Data: Compare both an average AND a spread measure.
Discrete & Continuous Data
What's the difference?
All numerical data falls into one of two types. Understanding which you're dealing with helps you choose the right method and interpret results correctly.
Discrete data can only take on specific, separate values. It's data you count.
Examples: number of pets (0, 1, 2, 3...), shoe sizes (6, 6.5, 7...), students in a class.
Continuous data can take any value within a range. It's data you measure.
Examples: height (could be 165.234... cm), weight, time, temperature.
How to tell the difference
Ask yourself: Do I need a scale or measuring tool to get this value?
- Yes (need to measure)? → Continuous.
- No (I count it)? → Discrete.
Example: Classify each type
(a) Time taken to swim 100 metres
Continuous. Time is measured with no constraints—it could be 45.3 seconds or 45.37 seconds.
(b) Time taken to the nearest hour to complete a task
Discrete. The question specifies "to the nearest hour," so only certain values are possible (1 hour, 2 hours, 3 hours...).
(c) Number of computers owned by each household
Discrete. You can't own 2.5 computers—only whole numbers.
Tip: Constraints = discrete. If a measurement says "to the nearest..." or "given to...", it's discrete. Unrestricted measurements = continuous.
Mean, Median & Mode
The Three Averages
An average is a single value that represents a typical value in a dataset. There are three different ways to measure it, and which one you use matters.
Mode – The Most Frequent Value
Definition
Mode = the value that appears most often
There can be more than one mode (bimodal). If no value repeats, there is no mode.
Example: In the dataset 1, 2, 2, 5, 6, the mode is 2 (appears twice).
Important: The mode is the value itself, NOT how many times it appears.
Median – The Middle Value
How to find it
1. Order all values from smallest to largest
2. Find the middle value
If there are an even number of values, the median is the average of the two middle values.
Example 1 (odd number):
Example 2 (even number):
Mean – The Average
Formula
Mean = Σx ÷ n
Example:
3
Comparing Data Sets