Mean Median Mode And Range — 3–5 Math | Scholars & Parents

What Is This?

When you have a set of data — test scores, heights, temperatures — single numbers can summarise the whole set. The three measures of centre (mean, median, mode) describe a "typical" value, and the range describes how spread out the data is.

Measure	What it tells you	How to find it
Mean	The average	Add all values, divide by how many there are
Median	The middle value	Order the data, find the middle
Mode	The most common value	Find the value that appears most often
Range	The spread	Largest value minus smallest value

Why Does It Matter?

Averages are everywhere: average test scores, average rainfall, average screen time, batting averages. Knowing which measure to use — and how each can mislead — is a core data literacy skill for school and life.

Part 1 — The Mean (Average)

How to Calculate

Mean = sum of all values ÷ number of values

Example: Find the mean of 4, 8, 6, 2.

Step 1 — add: 4 + 8 + 6 + 2 = 20
Step 2 — divide by the count (4 values): 20 ÷ 4 = 5 ✓

Example: Find the mean of 12, 15, 18, 11, 14.

Sum: 12 + 15 + 18 + 11 + 14 = 70
Mean: 70 ÷ 5 = 14 ✓

Working Backwards

If you know the mean and the count, you can find the total:

Total = mean × number of values

Example: The mean of 4 test scores is 80. What is the total of all scores?

Total = 80 × 4 = 320 ✓

Part 2 — The Median (Middle Value)

How to Calculate

Step 1: Put the values in order (smallest to largest). Step 2: Find the middle value.

Example (odd count): Find the median of 7, 2, 9, 4, 6.

Ordered: 2, 4, 6, 7, 9
Middle value (3rd of 5): 6 ✓

Example (even count): Find the median of 3, 8, 5, 10.

Ordered: 3, 5, 8, 10
Two middle values: 5 and 8
Median = (5 + 8) ÷ 2 = 6.5 ✓

With an even number of values, the median is the mean of the two middle values.

Part 3 — The Mode (Most Common)

How to Calculate

Count how often each value appears. The mode is the value that appears most often.

Example: Find the mode of 3, 7, 3, 9, 3, 5.

3 appears three times — more than any other value.
Mode = 3 ✓

Special cases:

Two modes (bimodal): 2, 2, 5, 7, 7 → modes are 2 and 7
No mode: 1, 2, 3, 4, 5 → every value appears once → no mode

Part 4 — The Range (Spread)

How to Calculate

Range = largest value − smallest value

Example: Find the range of 12, 5, 19, 8, 14.

Largest: 19, Smallest: 5
Range = 19 − 5 = 14 ✓

The range tells you how spread out the data is — a small range means values are close together; a large range means they vary widely.

All Four Together

Data set: 6, 3, 9, 6, 11

Measure	Working	Answer
Mean	(6+3+9+6+11) ÷ 5 = 35 ÷ 5	7
Median	Ordered: 3, 6, 6, 9, 11 → middle	6
Mode	6 appears twice	6
Range	11 − 3	8

Choosing the Right Measure

Mean uses every value — but one extreme value (outlier) can pull it strongly.
Median is resistant to outliers — good for skewed data like house prices.
Mode is best for categories (most popular shoe size, favourite colour).

Outlier example: Salaries 30, 32, 35, 38, 300 (thousands).

Mean = 435 ÷ 5 = 87 — misleadingly high!
Median = 35 — a much better "typical" value here.

Worked Examples

Worked Example 1: All four measures

Data: 5, 8, 5, 12, 10

Mean: (5+8+5+12+10) ÷ 5 = 40 ÷ 5 = 8
Median: ordered 5, 5, 8, 10, 12 → 8
Mode: 5 appears twice → 5
Range: 12 − 5 = 7

Worked Example 2: Even count median

Data: 4, 9, 2, 7, 6, 10

Ordered: 2, 4, 6, 7, 9, 10
Median = (6 + 7) ÷ 2 = 6.5

Worked Example 3: Working backwards

The mean of five numbers is 12. Four of the numbers are 10, 14, 9, and 15. What is the fifth number?

Total needed: 12 × 5 = 60
Sum of four known: 10 + 14 + 9 + 15 = 48
Fifth number: 60 − 48 = 12 ✓

Worked Example 4: Real-world

Daily temperatures for a week: 18, 21, 19, 23, 21, 20, 18 (°C)

Mean: 140 ÷ 7 = 20°C
Median: ordered 18, 18, 19, 20, 21, 21, 23 → 20°C
Mode: 18 and 21 both appear twice → bimodal: 18 and 21
Range: 23 − 18 = 5°C

Common Mistakes

Mistake 1: Forgetting to order the data before finding the median The median of 7, 2, 9 is NOT 2 (the middle as written). Order first: 2, 7, 9 → median = 7.

Mistake 2: Confusing mode and median Mode = most often. Median = middle (like the median strip in the middle of a road).

Mistake 3: Dividing by the wrong count for the mean Mean of 4, 8, 6, 2 is 20 ÷ 4 = 5 — divide by how many values there are (4), not by the largest value or any other number.

Mistake 4: Adding instead of subtracting for the range Range = largest − smallest, not largest + smallest.

Key Takeaways

Mean = sum ÷ count (the average; affected by outliers)
Median = middle of ordered data (use the mean of the two middle values for even counts)
Mode = most frequent value (there can be one mode, several, or none)
Range = largest − smallest (measures spread, not centre)
Always order the data before finding the median
Work backwards from the mean: total = mean × count

Practice and Resources

Ready to practise? Try our Grade 3-5 Mean, Median, Mode and Range Worksheet with practice on all four measures and working backwards. Test yourself with the Grade 3-5 Math Practice Test.