Averages (Mean, Median, Mode) — Grade 5 Mathematics
An average is a single value that represents a set of data. In Grade 5, we learn three measures of average: mean, median, and mode, and understand when each is most appropriate.
The Three Averages
Mean
The arithmetic average. Affected by very large or very small values.
Median
The middle of sorted data. Not affected by extreme values.
Mode
The value that appears most often. There can be more than one mode.
Finding the Median: Step by Step
Step 1 — Sort: 3, 3, 5, 6, 7, 8, 9
Step 2 — Find the middle (7 values → 4th value):
Median = 6 (highlighted). Mode = 3 (appears twice). Mean = (3+3+5+6+7+8+9) ÷ 7 = 41 ÷ 7 ≈ 5.86.
Worked Examples
Data: 4, 7, 4, 9, 6
- Mean: (4+7+4+9+6) ÷ 5 = 30 ÷ 5 = 6
- Sorted: 4, 4, 6, 7, 9 → Median = 6
- Mode = 4 (appears twice)
Find the median of: 12, 8, 15, 5, 9, 11
- Sorted: 5, 8, 9, 11, 12, 15
- Two middle values: 9 and 11
- Median = (9 + 11) ÷ 2 = 10
The mean of 5 test scores is 72. Four scores are 68, 75, 80, and 64. Find the missing score.
- Total needed = 72 × 5 = 360
- Sum of known = 68 + 75 + 80 + 64 = 287
- Missing score = 360 − 287 = 73
Practice Questions
1. Find the mean of: 5, 8, 3, 12, 7.
2. Find the median of: 14, 6, 9, 21, 3, 17, 11.
3. Find the mode of: 5, 3, 7, 5, 9, 3, 5, 1.
4. The mean of 4 numbers is 15. Three of the numbers are 12, 18, and 14. What is the fourth?
5. Find the median of: 2.3, 4.1, 1.8, 3.5, 2.9, 4.7.
Key Points to Remember
- Mean = sum ÷ count. Best for evenly distributed data.
- Median = middle value (sorted). Not affected by extreme values.
- Mode = most frequent. Can be used for non-numerical data (e.g., shoe sizes).
- Even number of values → median = mean of two middle values.
- To find a missing value: mean × count − known sum.