Cumulative Frequency Curves

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 – – – – – – 402

Solution Step 1: Find the class boundaries and the cumulative frequencies for each class. BoundariesFrequencyCumulative Frequency – – – – – –

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

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

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

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

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

Percentile Graphs KNOWWANTLEARN

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 – – – – – – 63 3

Solution Step 1: Find the class bound, c. f. and r. c. f. for each class. BoundariesFrequencyc.f.r.c.f. (%) – – – – – –

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

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

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

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

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.