Percentiles

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. $\mathrm{9.05}$.