2. © SNP Panpac (H.K.) Ltd. 11.4Cumulative Frequency Polygons and Curves Additional Example 4

3. © SNP Panpac (H.K.) Ltd. Additional Example 4 The table shows the times taken to run 400 m by 100 students. Time (s)Frequency 55.6 – 56.05 56.1 – 56.57 56.6 – 57.019 57.1 – 57.527 57.6 – 58.019 58.1 – 58.516 58.6 – 59.07

4. © SNP Panpac (H.K.) Ltd. Additional Example 4 (b)Draw a cumulative frequency polygon for the distribution. Solution (c)How many students ran 400 m over 58.05 s? (a)Construct a cumulative frequency table. Solution

5. © SNP Panpac (H.K.) Ltd. Additional Example 4 (f)Find the 10th percentile and 80th percentile of the times taken by the students. Solution (e)Find the median, lower and upper quartiles of the times taken by the students. Solution (d)If 40 students with the largest speed were selected to participate a competition, what was the time set as the standard of selection? Solution

6. © SNP Panpac (H.K.) Ltd. (a)Construct a cumulative frequency table. (b)Draw a cumulative frequency polygon for the distribution. (c)How many students ran 400 m over 58.05 s? (d)If 40 students with the largest speed were selected to participate a competition, what was the time set as the standard of selection? (e)Find the median, lower and upper quartiles of the times taken by the students. (f)Find the 10th percentile and 80th percentile of the times taken by the students. Solution Additional Example 4 (a) Q4(b) The table shows the times taken to run 400 m by 100 students. +5 +7 +19 +27 +19 +16 +7 Time (s)Frequency 55.6 – 56.05 56.1 – 56.57 56.6 – 57.019 57.1 – 57.527 57.6 – 58.019 58.1 – 58.516 58.6 – 59.07 Time less than (s) Cumulative Frequency 55.550 56.055 56.5512 57.0531 57.5558 58.0577 58.5593 59.05100

7. © SNP Panpac (H.K.) Ltd. Solution (b) Q4(c) (a)Construct a cumulative frequency table. (b)Draw a cumulative frequency polygon for the distribution. (c)How many students ran 400 m over 58.05 s? (d)If 40 students with the largest speed were selected to participate a competition, what was the time set as the standard of selection? (e)Find the median, lower and upper quartiles of the times taken by the students. (f)Find the 10th percentile and 80th percentile of the times taken by the students. Additional Example 4 The table shows the times taken to run 400 m by 100 students. Time (s)Frequency 55.6 – 56.05 56.1 – 56.57 56.6 – 57.019 57.1 – 57.527 57.6 – 58.019 58.1 – 58.516 58.6 – 59.07

8. © SNP Panpac (H.K.) Ltd. (a)Construct a cumulative frequency table. (b)Draw a cumulative frequency polygon for the distribution. (c)How many students ran 400 m over 58.05 s? (d)If 40 students with the largest speed were selected to participate a competition, what was the time set as the standard of selection? (e)Find the median, lower and upper quartiles of the times taken by the students. (f)Find the 10th percentile and 80th percentile of the times taken by the students. Solution (c)Number of students Q4(d) = 100 – 77 = 23 = 77 Additional Example 4 The table shows the times taken to run 400 m by 100 students. Time (s)Frequency 55.6 – 56.05 56.1 – 56.57 56.6 – 57.019 57.1 – 57.527 57.6 – 58.019 58.1 – 58.516 58.6 – 59.07

9. © SNP Panpac (H.K.) Ltd. (a)Construct a cumulative frequency table. (b)Draw a cumulative frequency polygon for the distribution. (c)How many students ran 400 m over 58.05 s? (d)If 40 students with the largest speed were selected to participate a competition, what was the time set as the standard of selection? (e)Find the median, lower and upper quartiles of the times taken by the students. (f)Find the 10th percentile and 80th percentile of the times taken by the students. Solution (d)The time for the cumulative frequency = 40 Q4(e) is 57.2 s.  The time must be less than 57.2 s. Additional Example 4 The table shows the times taken to run 400 m by 100 students. Time (s)Frequency 55.6 – 56.05 56.1 – 56.57 56.6 – 57.019 57.1 – 57.527 57.6 – 58.019 58.1 – 58.516 58.6 – 59.07

10. © SNP Panpac (H.K.) Ltd. Solution Q4(f) (e) The times for the cumulative frequencies = 25, 50 and 75 (a)Construct a cumulative frequency table. (b)Draw a cumulative frequency polygon for the distribution. (c)How many students ran 400 m over 58.05 s? (d)If 40 students with the largest speed were selected to participate a competition, what was the time set as the standard of selection? (e)Find the median, lower and upper quartiles of the times taken by the students. (f)Find the 10th percentile and 80th percentile of the times taken by the students. Additional Example 4 The table shows the times taken to run 400 m by 100 students. Time (s)Frequency 55.6 – 56.05 56.1 – 56.57 56.6 – 57.019 57.1 – 57.527 57.6 – 58.019 58.1 – 58.516 58.6 – 59.07 are 56.9 s, 57.4 s and 58 s respectively.

11. © SNP Panpac (H.K.) Ltd. Solution Lower quartile = 56.9 s Upper quartile = 58 s Q4(f)  Median = 57.4 s (a)Construct a cumulative frequency table. (b)Draw a cumulative frequency polygon for the distribution. (c)How many students ran 400 m over 58.05 s? (d)If 40 students with the largest speed were selected to participate a competition, what was the time set as the standard of selection? (e)Find the median, lower and upper quartiles of the times taken by the students. (f)Find the 10th percentile and 80th percentile of the times taken by the students. Additional Example 4 The table shows the times taken to run 400 m by 100 students. Time (s)Frequency 55.6 – 56.05 56.1 – 56.57 56.6 – 57.019 57.1 – 57.527 57.6 – 58.019 58.1 – 58.516 58.6 – 59.07

12. © SNP Panpac (H.K.) Ltd. Solution (f) are 56.4 s and 58.15 s respectively. (a)Construct a cumulative frequency table. (b)Draw a cumulative frequency polygon for the distribution. (c)How many students ran 400 m over 58.05 s? (d)If 40 students with the largest speed were selected to participate a competition, what was the time set as the standard of selection? (e)Find the median, lower and upper quartiles of the times taken by the students. (f)Find the 10th percentile and 80th percentile of the times taken by the students. Additional Example 4 The table shows the times taken to run 400 m by 100 students. Time (s)Frequency 55.6 – 56.05 56.1 – 56.57 56.6 – 57.019 57.1 – 57.527 57.6 – 58.019 58.1 – 58.516 58.6 – 59.07 The time for the cumulative frequencies = 10 and 80

13. © SNP Panpac (H.K.) Ltd. Solution  The 10th percentile = 56.4 s The 80th percentile = 58.15 s (a)Construct a cumulative frequency table. (b)Draw a cumulative frequency polygon for the distribution. (c)How many students ran 400 m over 58.05 s? (d)If 40 students with the largest speed were selected to participate a competition, what was the time set as the standard of selection? (e)Find the median, lower and upper quartiles of the times taken by the students. (f)Find the 10th percentile and 80th percentile of the times taken by the students. Additional Example 4 The table shows the times taken to run 400 m by 100 students. Time (s)Frequency 55.6 – 56.05 56.1 – 56.57 56.6 – 57.019 57.1 – 57.527 57.6 – 58.019 58.1 – 58.516 58.6 – 59.07