Mean
Sum of values รท number of values.
๐ฏ Learning Objectives
- calculate mean, median and mode;
- order data before finding the median;
- recognise more than one mode or no mode;
- compare the three measures;
- choose the most suitable average.
Introduction
This lesson develops Mean, Median and Mode from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
Three Measures
Median
Middle value after ordering.
Mode
Most frequent value.
Worked Example
Data: 2, 3, 3, 5, 12.
Mean=25รท5=5, median=3, mode=3.
The high value 12 pulls the mean upward. The median may describe the typical value better.
๐ข Mean, Median and Mode Calculator
Meanโ
Medianโ
Modeโ
Rangeโ
Practice Questions
- Find mean, median and mode of 4,6,6,7,12.
- Find the median of 9,2,5,7,4,8.
- Data are 1,2,3,4. State the mode.
- Which average is usually most affected by an extreme value?
- Explain why median income may be preferred to mean income.
โ Check Your Work
Show answers and working
- Mean=35รท5=7, median=6, mode=6.
- Ordered: 2,4,5,7,8,9. Median=(5+7)รท2=6.
- There is no mode because no value repeats.
- The mean.
- Very high incomes can pull the mean upward; the median better represents the middle person.
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Choose the average that answers the context fairly.
- Always order data before finding the median.