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. \(\mathrm{9.05}\).