Standard Deviation, Quartiles & Percentiles • Topic 3 of 4

Percentiles

A percentile is about rank, not score. Being in the 90th percentile means about 90% of the data falls at or below your value — it does not mean you scored 90%. This distinction is the heart of nearly every GRE percentile question, and it is exactly how test scores like the GRE itself are reported. Percentiles connect neatly to quartiles: Q1 is the 25th percentile, the median is the 50th, and Q3 is the 75th. Two things to keep straight. First, a high percentile with a low raw score is entirely possible on a hard test where everyone scored low — percentile depends on the surrounding distribution, not on some fixed scale. Second, "the difference between the 80th and 90th percentiles" is a difference in rank position, and the corresponding gap in actual values can be large or small depending on how bunched the data is at that end. Read the words carefully: "percentile" signals a position in the ordered data.

✅ Solved examples

1. In a group of 200 test-takers, a score is at the 75th percentile. About how many people scored at or below it?
75th percentile means about 75% fall at or below. 0.75 × 200 = 150 people.
2. A student is in the 90th percentile on a test where the top raw score was 62 out of 100. Did the student answer 90% correctly?
Not necessarily. The 90th percentile means the student outranked about 90% of test-takers; the raw score could be well under 90%. Percentile measures rank, not the fraction correct.
3. A data set of 40 values is sorted. Which percentile corresponds to the value with 30 values at or below it?
30/40 = 0.75 = 75%. The value sits at roughly the 75th percentile, i.e. Q3.
4. Quantitative Comparison. On a national exam, Student X is at the 60th percentile and Student Y is at the 80th percentile. Quantity A: X's raw score. Quantity B: Y's raw score. Which is greater?
A higher percentile means a higher rank, so Y ranks above X and Y's raw score is at least as high — in a strictly ordered ranking, higher. Quantity B is greater. (This is a rare QC where percentile order does fix the score order.)

✏️ Practice — try these, take hints as needed

1. In 500 applicants, roughly how many rank at or below the 40th percentile?
40th percentile = about 40% at or below.
0.40 × 500.
Multiply.
about 200
2. The median of a data set is the ___th percentile.
Half the data lies below the median.
50% at or below.
State the number.
50th
3. Q3 corresponds to which percentile?
Q3 is the third quartile.
Three quarters of the data lies at or below it.
3/4 as a percent.
75th
4. True or false: a student in the 95th percentile answered 95% of questions correctly.
Percentile is about rank among test-takers.
It is not the fraction correct.
Consider a very hard test.
False
5. Of 250 scores, a value has 50 scores below it. Roughly which percentile?
50 out of 250.
50/250 = 0.20.
As a percent.
20th percentile

📝 Topic test — 8 questions

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