Statistics / Unit 3: The Normal Distribution
3.3 Percentiles
Notes
The percentile of a value is the percent of the data that are at or below it.
- A value at the 80th percentile is at or above $80\%$ of the data (and below about $20\%$).
- In a normal distribution, $z = 0$ is the 50th percentile, $z = 1$ is about the 84th and $z = -1$ is about the 16th.
- Percentiles describe position, not the score itself. Scoring in the 90th percentile does not mean you answered $90\%$ correctly.
- Example: With 200 students and a score at the 75th percentile, about $0.75 \times 200 = 150$ students scored at or below it.
Practice
A student is at the 90th percentile on a state test. This means:
A percentile is a position in the distribution.
In a normal distribution, a value with $z = 0$ is at the:
The mean equals the median in a normal distribution, so half the values are below it.
Of 200 students, a score is at the 75th percentile. About how many students scored at or below it?
$0.75 \times 200 = 150$.
Ready for more? Take the Unit 3 test.