Statistics Fundamentals • Topic 1 of 6

Mean

The mean (average) is the sum of all the values divided by how many there are. It balances the data and is sensitive to every value, so a single very large or very small number can pull it noticeably. Useful rearrangements appear often on the SAT: the sum equals mean × count, so if you know the average and the number of values you can recover the total, or find a missing value. Adding a new value equal to the current mean leaves the mean unchanged. Recognising "average = total ÷ count" in both directions is the key skill.

✅ Solved examples

1. Find the mean of 4, 8, 10, 14.
Sum = 36; divide by 4: mean = 9.
2. The mean of 5 numbers is 12. What is their sum?
Sum = mean × count = 12 × 5 = 60.
3. Four tests average 80. A fifth score of 90 is added. New mean?
Total = 320 + 90 = 410; divide by 5 = 82.
4. The mean of 3, 7, x is 6. Find x.
Sum must be 18; 3 + 7 + x = 18, so x = 8.

✏️ Practice — try these, take hints as needed

1. Find the mean of 6, 9, 12, 13.
Add the values.
Sum = 40.
Divide by 4.
10.
2. The mean of 6 numbers is 15. What is their sum?
Sum = mean × count.
15 × 6.
—
90.
3. The mean of 4, 8, x is 7. Find x.
Sum must be 21.
4 + 8 + x = 21.
—
9.
4. Five numbers average 20. One more, equal to 20, is added. New mean?
Adding a value equal to the mean.
The mean is unchanged.
—
20.
5. Three numbers have mean 10; two of them are 8 and 9. Find the third.
Total = 30.
30 − 8 − 9.
—
13.

📝 Topic test — 8 questions

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