Percentiles Statistics Example 3

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Example 3

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

Solution

  1. 1
    The percentile rank indicates the percentage of values that fall below a given score.
  2. 2
    Use the formula: Percentile=Number of values belowTotal number of values×100\text{Percentile} = \frac{\text{Number of values below}}{\text{Total number of values}} \times 100
  3. 3
    Substitute: Percentile=3240×100=80th percentile\text{Percentile} = \frac{32}{40} \times 100 = 80\text{th percentile}

Answer

The student is at the 80th percentile.
Being at the 80th percentile means the student scored higher than 80% of the class. Equivalently, only 20% of students scored higher. Percentiles are commonly used in standardized testing to compare individual performance against a reference group.

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 1 easy

A student scored in the 85th percentile on a standardised test with 200 test-takers. What does this

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 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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