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3. Find the scores with Rank I_R and with Rank I_R + 1. For this example, this means the score with Rank 2 and the score with Rank 3. The scores are 5 and 7.

4. Interpolate by multiplying the difference between the scores by F_R and add the result to the lower score. For these data, this is (0.25)(7 - 5) + 5 = 5.5.

Therefore, the 25th percentile is 5.5. If we had used the first definition (the smallest score greater than 25% of the scores), the 25th percentile would have been 7. If we had used the second definition (the smallest score greater than or equal to 25% of the scores), the 25th percentile would have been 5.

For a second example, consider the 20 quiz scores shown in Table 2.

Table 2. 20 Quiz Scores.

We will compute the 25th and the 85th percentiles. For the 25th,

$R={\frac {25}{100}}\times (20+1)={\frac {21}{4}}=5.25$

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