Percentiles Statistics Example 2

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

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, 50, 55, 60, 65, 70. Find the value at the 40th percentile.

Solution

  1. 1
    Step 1: Calculate the position: L=P100×n=40100×20=8L = \frac{P}{100} \times n = \frac{40}{100} \times 20 = 8.
  2. 2
    Step 2: Since L=8L = 8 is a whole number, the 40th percentile is the average of the 8th and 9th values.
  3. 3
    Step 3: 8th value = 30, 9th value = 32. P40=30+322=31P_{40} = \frac{30 + 32}{2} = 31.

Answer

The 40th percentile is 31.
To find a percentile, calculate the position in the sorted data using L=P100×nL = \frac{P}{100} \times n. When LL is a whole number, average the LLth and (L+1)(L+1)th values. When LL is not whole, round up to the next integer position.

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 →

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