Quantitative Aptitude – Average
Goal: Know what “average” means, how to find it, and when it’s useful.
1. What is an Average?
- Average is a single number that represents the “middle” or “typical” value of a set of numbers.
- Think of it as the number you would give to each item if you spread the total equally among them.
Everyday analogy
Imagine you have 5 friends who each bring a different number of candies to a party.
If you add all the candies together and then split them equally, the number each friend gets is the average number of candies.
2. How to Calculate the Average
Step‑by‑Step
- Add up all the numbers in the set.
- Count how many numbers there are.
- Divide the sum by the count.
[ \text{Average} = \frac{\text{Sum of all numbers}}{\text{Number of items}} ]
Tiny Example
| Test Score | 70 | 80 | 90 | 60 | 85 |
|---|---|---|---|---|---|
| Sum | 405 | ||||
| Count | 5 | ||||
| Average | 81 |
- Sum = 70 + 80 + 90 + 60 + 85 = 405
- Count = 5
- Average = 405 ÷ 5 = 81
So the average score is 81.
3. Why Use the Average?
| Situation | Average Helps |
|---|---|
| Compare performance of two groups | Gives a single number to compare |
| Estimate typical value | Gives a sense of what’s “normal” |
| Check fairness of distribution | Helps spot outliers that skew results |
4. Common Mistakes
| Mistake | Fix |
|---|---|
| Forgetting to divide by the count | After adding, always divide by how many numbers you added. |
| Using “average” when numbers are very skewed | If one number is much larger or smaller, consider median or mode instead. |
| Adding zeros as if they are real data | Only include real observations. |
5. Quick Practice Problems
-
Averages of two groups
Group A scores: 75, 85, 90
Group B scores: 60, 70, 80, 90
What is the overall average? -
Daily Temperature
Temperatures (°C) for a week: 22, 24, 19, 23, 25, 21, 20
Find the average temperature. -
Average Speed
A car travels 120 km in 2 hours, 90 km in 1.5 hours, and 150 km in 3 hours.
What is the overall average speed?
(Hint: Total distance ÷ Total time)
6. Key Takeaways
- Average = total ÷ count
- It’s a simple but powerful way to summarize data.
- Use it when you need a quick “typical” value.
- Remember the pitfalls: don’t mix it with “median” or “mode” unless you’re sure it’s the right tool.
You’re ready to tackle any average‑related question on the MCAT!