Averages
Calculate mean; find missing values from average.
Averages
Averages (Mean)
What you'll learn
- To calculate the mean (average) of a set of numbers: total ÷ count.
- To find a missing value when the average and other values are known.
- To interpret average in real contexts — runs per innings, daily temperature, marks per test.
- To connect with NCERT Math-Magic 5, Chapter 12 (Smart Charts) and everyday "fair share" ideas.
Key concepts
Level 1 — Mean formula
Verbal: The average is what each member would get if the total were shared equally.
Symbolic: Mean = (Sum of all values) ÷ (Number of values)
| Data set | Sum | Count | Mean |
|---|---|---|---|
| 4, 6, 8, 10 | 28 | 4 | 7 |
| 15, 20, 25 | 60 | 3 | 20 |
| 12, 18 | 30 | 2 | 15 |
NCERT link: Math-Magic 5, Ch 12 — average pages read per day, average height of plants.
Level 2 — Missing value problems
Verbal: If average of four numbers is 10, total = 4 × 10 = 40. Subtract known values to find the missing one.
Real-life: Four friends spent ₹90, ₹110, ₹100 on snacks. Average = 300 ÷ 3 = ₹100 each if shared equally.
Symbolic: Missing value = (Mean × n) − (sum of known values)
| Given | Find |
|---|---|
| Average of 5 tests = 80, four scores 75, 82, 78, 85 | Fifth score |
| Average daily steps 6000 for 7 days, total for 6 days known | Day 7 steps |
Worked example
Runs in 5 innings: 45, 30, 60, 15, 50. Find average.
Step 1 — Sum: 45 + 30 + 60 + 15 + 50 = 200
Step 2 — Count: 5 innings
Step 3 — Mean: 200 ÷ 5 = 40
Answer: 40 runs per innings (average)
Average of 4 numbers is 25. Three numbers are 20, 22, 28. Find the fourth.
Step 1 — Total needed: 4 × 25 = 100
Step 2 — Sum of three: 20 + 22 + 28 = 70
Step 3 — Fourth: 100 − 70 = 30
Answer: 30
Common mistakes
| Mistake | Why it happens | Fix |
|---|---|---|
| Dividing by wrong count | Forgetting one value | Count every data point |
| Average = middle number always | Confusing mean with median | Mean = total ÷ count |
| Adding averages directly | Mean of 10 and 20 ≠ 15 if counts differ | Weight by group sizes in advanced cases |
| Rounding too early | Losing precision in multi-step | Keep full sum until final division |
Quick check
- Mean of 12, 15, 18, 21?
- Average of 5 numbers is 14. What is their sum?
- Scores: 8, 10, ?, 12; average = 10. Find ?.
- Stretch: Class average on a test is 72 for 30 students. Total marks obtained?
Revision tip: Link "average" to "fair share" — if 4 friends share ₹200 equally, each gets ₹50. That ₹50 is the mean of their individual amounts when total is known.
Open the Practice tab for graded questions on Averages.
Key Takeaways (TL;DR)
- What you'll learn
- Key concepts
- Worked example
- Common mistakes
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