1. Cumulative Frequency Curves

2. Example 1 The heights of some plants grown in a laboratory were recorded as follows: Construct a cumulative frequency graph and then answer the questions that follow. Height (cm) Frequency 11 – 153 16 – 207 21 – 2519 26 – 3020 31 – 3511 36 – 402

3. Solution Step 1: Find the class boundaries and the cumulative frequencies for each class. BoundariesFrequencyCumulative Frequency 3 7 19 20 11 2 10.5 – 15. 5 15.5 – 20.5 20.5 – 25.5 25.5 – 30.5 30.5 – 35.5 35.5 – 40.5 3 10 29 49 60 62

4. Step 2: Scale off your x and y axes….x-axis with class boundaries….y-axis with appropriate scaling to accommodate the cumulative frequencies.5

5. Step 3: Plot the cumulative frequency of each class at the UPPER CLASS BOUNDARY.5

6. Step 4: Starting at the lowest class boundary (frequency = 0) connect all of your points to create your graph..5

7. 1) Approximately how many plants had a height less than 25 cm? 2) 55 plants had a height less than ____ cm?

8. Measures of Position - Percentile Graphs Definition: indicate the position of a value in a data set in hundredths. Used frequently in education and health related fields. Essential Question: Why do we study percentile graphs? Growth charts

9. Percentile Graphs KNOWWANTLEARN

10. Example 2 The following data represent vehicle speeds on a highway: Construct a percentile graph (or a relative cumulative frequency graph) and then answer the questions that follow. Speed (mph) Frequency 46 – 48 1 49 – 51 3 52 – 54 6 55 – 57 15 58 – 60 22 61 – 63 3

11. Solution Step 1: Find the class bound, c. f. and r. c. f. for each class. BoundariesFrequencyc.f.r.c.f. (%) 1 3 6 15 22 3 45.5 – 48.5 48.5 – 51.5 51.5 – 54.5 54.5 – 57.5 57.5 – 60.5 60.5 – 63.5 1 4 10 25 47 50 2 8 20 50 94 100

12. Step 2: Scale off your x and y axes….x-axis with class boundaries….y-axis by percents..5

13. Step 3: Plot the relative cumulative frequency of each class at the UPPER CLASS BOUNDARY.5

14. Step 4: Starting at the lowest class boundary (frequency = 0) connect all of your points to create your graph.

15. 1)What percentage of drivers were traveling at a speed greater than 55 mph? 2) 70% of drivers were traveling under what speed?

16. Lesson Summary Ticket out the door: Describe the process for constructing a proper percentile graph to your partner. Make sure you include the type of data set and all criteria necessary for construction of the graph.