Percentiles Statistics Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
A student scored in the 85th percentile on a standardised test with 200 test-takers. What does this mean and how many students scored lower?

Solution

  1. 1
    Step 1: The 85th percentile means the student scored higher than 85% of all test-takers.
  2. 2
    Step 2: Number who scored lower: 200×0.85=170200 \times 0.85 = 170 students.
  3. 3
    Step 3: This means 200−170=30200 - 170 = 30 students scored the same or higher.

Answer

The student scored higher than 170 out of 200 test-takers (85%). 30 students scored the same or higher.
A percentile indicates the percentage of values in a distribution that fall below a given value. Being in the 85th percentile does not mean the student scored 85% on the test — it means they outperformed 85% of the other test-takers.

About Percentiles

Percentiles are values that divide a ranked distribution into 100 equal parts. The nnth percentile is the value below which n%n\% of the data falls, telling you where a specific observation stands relative to the entire dataset.

Learn more about Percentiles →

More Percentiles Examples

Example 2 medium

Given the sorted data set of 20 values: 12, 15, 18, 20, 22, 25, 27, 30, 32, 35, 38, 40, 42, 45, 48,

Example 3 medium

In a class of 40 students, a student scored higher than 32 others. What percentile is the student at

Example 4 medium

A baby's weight is at the 25th percentile for her age group. Her parents are worried she is underwei

Example 5 hard

In a normally distributed data set with mean 500 and standard deviation 100, approximately what valu

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