SAT Math: Mean (Average)
41+ practice questions in Praczo
The concept, explained
- 1
Mean = sum of all values ÷ count of values. Rearranged: Sum = Mean × n. The SAT uses this rearrangement constantly.
- 2
The SAT often gives you a mean and asks for a missing value. Compute the required total sum, then find the missing piece.
- 3
Weighted mean: when combining groups of different sizes, you cannot simply average the group means. Compute each group's total, add them, then divide by the total count.
- 4
Adding a constant c to every value shifts the mean by c. Multiplying every value by c scales the mean by c.
- 5
The mean is sensitive to outliers — one extreme value will pull it significantly. This is why mean and median are tested together.
- ✗ Averaging group means when the groups are different sizes: if Group A has mean 10 (n=5) and Group B has mean 20 (n=15), the overall mean is not 15 — compute (50 + 300)/20 = 17.5.
- ✗ Forgetting Sum = Mean × n when a value is added or removed and the problem gives you the new mean.
SAT-style practice
The mean of a set of 8 numbers is 15. A ninth number is added, and the new mean is 14. What is the ninth number?
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