Percentiles: Answers | Saylor Academy

Percentiles

This section discusses percentiles, which are useful for describing relative standings of observations in a dataset.

Answers

1. According to Definition 1, the 25th percentile is the lowest score higher than 25% of the scores. Since there are $\mathrm{8}$ scores, this would be the lowest score higher than $(0.25 \times 8 = 2 \, \mathrm{scores}$ . The score $\mathrm{7}$ is higher than the scores $\mathrm{3}$ and $\mathrm{5}$ .

2. According to Definition 2, the 25th percentile is the lowest number greater than or equal to 25% of the scores. Since there are

$\mathrm{8}$ scores, this would be the lowest number greater than or equal to

$(0.25) \times 8 = 2 \, \mathrm{scores}$ . The number 5 is greater than or equal to the scores

$\mathrm{3}$ and

$\mathrm{5}$ .

3. $\mathrm{R} =25 / 100 \times (8 + 1) = 2.25 ;$ $\mathrm{IR} =2$ ; $\mathrm{FR} = 0.25$ ; The $\mathrm{25th \, percentile} = 0.25 \times (7-5) + 5 = 5.5$

4. $\mathrm{R} =80 / 100 \times (8+1)=7.2 ; \mathrm{IR} =7 ; \mathrm{FR} =0.2 ;$ The $\mathrm{80th \, percentile} = 0.2 \times (30-25)+25=26$

5.

$\mathrm{11.19}$ .

6.

$\mathrm{9.05}$ .

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