πŸ“Š Averages

Mean, Median, Mode and Range – make sense of data sets!

πŸ“– Learn
Averages concepts
✏️ Examples
Worked problems
πŸ”¬ Visualiser
Interactive tools
🎯 Practice
20 mixed questions

πŸ“– Averages

1. Mean

The mean is the most common type of average. Add all the values together, then divide by how many values there are.

Mean = Sum of all values Γ· number of values
Mean = Ξ£x Γ· n

Example: Data set {3, 5, 7, 9, 6} β†’ Sum = 30, n = 5 β†’ Mean = 30 Γ· 5 = 6

2. Median

The median is the middle value when data is sorted in order.

For odd count: middle value
For even count: mean of two middle values

Odd example: {3, 5, 7, 9, 11} β†’ Median = 7

Even example: {2, 4, 6, 8, 10, 12} β†’ Median = (6+8)Γ·2 = 7

Always sort the data first before finding the median!

3. Mode

The mode is the value that appears most often in the data set.

Mode = most frequent value

Example: {3, 5, 3, 7, 3, 9} β†’ 3 appears 3 times β†’ Mode = 3

There can be more than one mode (bimodal) or no mode if all values appear equally.

4. Range

The range measures the spread of the data β€” how far apart the highest and lowest values are.

Range = Maximum value βˆ’ Minimum value

Example: {3, 7, 12, 1, 9} β†’ Max = 12, Min = 1 β†’ Range = 12 βˆ’ 1 = 11

5. Choosing the Right Average

AverageBest used when…Watch out for…
MeanData is spread evenlyAffected by very high/low values (outliers)
MedianData has outliers (e.g. salaries)Ignores all other values
ModeFinding most popular item (e.g. shoe size)May not exist or not be representative

Range is not an average β€” it tells us about the spread of the data.

✏️ Worked Examples

Example 1 – Finding the Mean

Find the mean of: 4, 8, 6, 10, 12

Step 1: Add all values β†’ 4 + 8 + 6 + 10 + 12 = 40
Step 2: Count how many values β†’ n = 5
Step 3: Mean = Sum Γ· n = 40 Γ· 5 = 8

Example 2 – Finding the Median

Find the median of: 7, 2, 9, 4, 11, 6, 3

Step 1: Sort in order β†’ 2, 3, 4, 6, 7, 9, 11
Step 2: n = 7 (odd) β†’ middle position = 4th value
Step 3: Median = 6

Even count: {2, 4, 6, 8, 10, 12} β†’ middle two = 6 and 8 β†’ Median = (6+8)Γ·2 = 7

Example 3 – Finding the Mode and Range

Data: 5, 8, 3, 8, 5, 8, 2

Step 1 (Mode): Count frequencies β†’ 5 appears 2Γ—, 8 appears 3Γ—, 3 appears 1Γ—, 2 appears 1Γ—
Step 2: Most frequent = 8 β†’ Mode = 8
Step 3 (Range): Max = 8, Min = 2 β†’ Range = 8 βˆ’ 2 = 6

Example 4 – Finding a Missing Value

Five numbers have a mean of 10. Four of them are 8, 9, 11, 12. Find the fifth number.

Step 1: Total sum needed = Mean Γ— n = 10 Γ— 5 = 50
Step 2: Sum of known values = 8 + 9 + 11 + 12 = 40
Step 3: Missing value = 50 βˆ’ 40 = 10

πŸ”¬ Averages Visualiser

Averages Calculator

Enter comma-separated numbers:

Mean Finder




Missing Value Finder

Enter known values (comma-separated) and desired mean:



Exercise 1 – Mean

Find the mean of each data set.

Exercise 2 – Median

Find the median of each data set. Sort first if needed!

Exercise 3 – Mode

Find the mode of each data set.

Exercise 4 – Range

Find the range of each data set.

Exercise 5 – Mixed

Use mean, median, mode and range as directed.

🎯 Practice – 20 Questions

πŸ† Challenge