SECTION 2.1 Frequency Distributions and Their Graphs 47 Upper class boundary f Cumulative frequency 190.5 3 3 226.5 2 5 262.5 5 10 298.5 6 16 334.5 7 23 370.5 4 27 406.5 3 30 Constructing an Ogive (Cumulative Frequency Graph) 1. Construct a frequency distribution that includes cumulative frequencies as one of the columns. 2. Specify the horizontal and vertical scales. The horizontal scale consists of upper class boundaries, and the vertical scale measures cumulative frequencies. 3. Plot points that represent the upper class boundaries and their corresponding cumulative frequencies. 4. Connect the points in order from left to right with line segments. 5. The graph should start at the lower boundary of the first class (cumulative frequency is 0) and should end at the upper boundary of the last class (cumulative frequency is equal to the sample size). GUIDELINES Constructing an Ogive Draw an ogive for the frequency distribution in Example 2. SOLUTION Using the cumulative frequencies, you can construct the ogive shown. The upper class boundaries, frequencies, and cumulative frequencies are shown in the table. Notice that the graph starts at 154.5, where the cumulative frequency is 0, and the graph ends at 406.5, where the cumulative frequency is 30. 5 154.5 190.5 226.5 262.5 298.5 334.5 370.5 406.5 10 15 20 25 30 Times (in minutes) Cumulative frequency (number of adults) Cell Phone Screen Times Interpretation From the ogive, you can see that 10 adults had screen times of 262.5 minutes or less. Also, the greatest increase in cumulative frequency occurs between 298.5 minutes and 334.5 minutes because the line segment is steepest between these two class boundaries. TRY IT YOURSELF 6 Use the frequency distribution from Try It Yourself 2 to construct an ogive that represents the points scored by the 55 winning teams listed on page 39. Answer: Page A36 Another type of ogive uses percent as the vertical axis instead of frequency (see Example 5 in Section 2.5). EXAMPLE 6
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