Word Problems Involving Averages
SAT Math — Statistics & Data Analysis
High-Frequency SAT Topic
1. The Core Formula
Every average (mean) word problem on the SAT revolves around one fundamental relationship:
$$\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}$$
The key rearrangement that unlocks most problems is:
$$\text{Sum} = \text{Mean} \cdot \text{Number of values}$$
Three Quantities
- ✅ Sum (S)
- ✅ Mean (M)
- ✅ Count (N)
If you know any two, you can find the third: $S = M \cdot N$
Strategy
- Identify what is known and what is unknown.
- Convert every average into a sum using $S = M \cdot N$.
- Set up an equation and solve.
2. Finding a Missing Value Given the Mean
Method: Multiply the mean by the total count to find the required sum, then subtract the sum of known values.
Example: The average of 5 numbers is 18. Four of the numbers are 14, 20, 16, and 22. Find the missing number.
- Required sum $= 5 \cdot 18 = 90$
- Sum of known values $= 14 + 20 + 16 + 22 = 72$
- Missing number $= 90 - 72 = \boxed{18}$