- Define and explain Averages and range in your own words
- Use key terms such as Median accurately
- Apply what you have learned to new examples and questions
- Avoid the common mistakes learners make with this topic
Statistics turns raw data into decisions — but only when it is done honestly. These lessons teach you to summarise data with averages, display it clearly, and spot when a graph is trying to fool you.
This lesson focuses on Averages and range: mean, median, mode and range, and which average suits which situation.
Mean, median, mode and range, and which average suits which situation.
Key ideas
Choosing an average
Use the mean for symmetric data with no extremes, the median when a few extreme values would distort the mean (such as salaries), and the mode for categories (such as favourite colours). Always consider the range too, since identical averages can hide very different spreads.
Correlation is not causation
A strong correlation only shows that two things vary together; a third factor may cause both. A line of best fit drawn through the middle of the points shows the trend and can estimate values within the data range, but never extrapolate far beyond it.
Key term — Median: The middle value when data is ordered from smallest to largest; a robust average unaffected by extreme values.
Find the mean, median, mode and range of: 3, 5, 5, 8, 9.
Mean: (3 + 5 + 5 + 8 + 9) ÷ 5 = 30 ÷ 5 = 6. Median: the data is ordered; the 3rd of 5 values is 5. Mode: 5 appears most often (twice). Range: 9 − 3 = 6.
Answer: Mean 6, median 5, mode 5, range 6.
- Finding the median without ordering the data Always sort the values first; the median is the middle of the ordered list, not the middle of the original list.
- Forgetting that an even count has no single middle value With an even number of values, the median is halfway between the two middle values, e.g. (6 + 8) ÷ 2 = 7.
Practice
The median (7.5); the mean (12.5) is distorted by the outlier 40.
Mode = 6; range = 6 − 2 = 4.
Ordered: 2, 4, 7, 9, 11; median = 7.
Sum = 50; mean = 50 ÷ 5 = 10.
Quick check
Which of these best defines "Median"?
Why might a bar chart with a y-axis starting at 50 be misleading?
A scatter diagram shows points rising left to right. What type of correlation is this?
- Averages and range: mean, median, mode and range, and which average suits which situation.
- Choosing an average: Use the mean for symmetric data with no extremes, the median when a few extreme values would distort the mean (such as salaries), and the mode for categories (such as favourite colours).
- Mean: The total of all values divided by how many values there are; the most common average, but sensitive to extreme values.
- Watch out for: finding the median without ordering the data