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.

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

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

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