Page:Online Statistics Education.pdf/31

 3. Find the scores with Rank IR and with Rank IR + 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 FR 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,

$$R=\frac{25}{100}\times(20+1)=\frac{21}{4}=5.25$$ 31