Page:Online Statistics Education.pdf/32

 $$IR=5$$ $$and$$ $$FR=0.25.$$

Since the score with a rank of IR (which is 5) and the score with a rank of IR + 1 (which are both equal to 5, the 25th percentile is 5. In terms of the formula:

$$25th$$ $$percentile=(.25)\times(5-5)+5=5.$$

For the 85th percentile,

$$R=\frac{85}{100}\times(20+1)=17.85$$

$$IR=17$$ $$and$$ $$FR=0.85$$


 * Caution: FR does not generally equal the percentage to be computed as it does here.

The score with a rank of 17 is 9 and the score with a rank of 18 is 10. Therefore, the 85th percentile is:

$$(0.85)(10-9)+9=9.85$$

Consider the 50th percentile of the numbers 2, 3, 5, 9.

$$R=\frac{50}{100}\times(4+1)=2.5$$

$$IR=2$$ $$and$$ $$FR=0.5$$

The score with a rank of IR is 3 and the score with a rank of IR + 1 is 5. Therefore, the 50th percentile is:

$$(0.5)(5-3)+3=4$$

Finally, consider the 50th percentile of the numbers 2, 3, 5, 9, 11.

$$R=\frac{50}{100}\times(5+1)=3$$

$$IR=3$$ $$and$$ $$FR=0.$$ 32