Round each observation to the nearest tenth of a cent and draw a stem and leaf plot.

Transcription

1 Warm Up Round each observation to the nearest tenth of a cent and draw a stem and leaf plot. 1. Constructing Frequency Polygons 2. Create Cumulative Frequency and Cumulative Relative Frequency Tables 3. Construct Ogives 4. Draw Time Series Graphs 1

2 1. Constructing Frequency Polygons A frequency polygon is drawn by plotting a point above each class midpoint and connecting the points with a straight line. Two additional line segments are drawn connecting each end of the graph with the horizontal axis. Class midpoints are found by averaging successive lower class limits. 1. Constructing Frequency Polygons Remember the "average commute" data from the last section? 2

3 1. Constructing Frequency Polygons 2. Create Cumulative Frequency and Cumulative Relative Frequency Tables Cumulative tables show the sum of values up to and including that particular category. As with regular tables, we can have both cumulative frequency and relative frequency. For discrete data, it displays the total number of observations less than or equal to the category. For continuous data, it displays the total number of observations less than or equal to the upper class limit of a class Cumulative Frequency 3

4 2. Create Cumulative Frequency and Cumulative Relative Frequency Tables Cumulative Relative Frequency 3. Construct Ogives An ogive (read as "oh jive") is a graph that represents the cumulative frequency or cumulative relative frequency for the class. It is constructed by plotting points the x coordinates are the upper class limits and the y coordinate is the corresponding cumulative frequency or cumulative relative frequency. Here is a ogive for the commute data from the previous slide. Based on this ogive, which interval saw the greatest frequency? 4

5 3. Construct Ogives The table represents the 3 year rate of return (in percent, adjusted for sales charges) for a simple random sample of 40 small capitalization growth mutual funds. Let's complete the cumulative frequency and relative frequency columns. Then lets use them to construct a cumulative frequency ogive. 3. Construct Ogives 5

6 SAT Writing Scores The following frequency ogive represents the SAT writing scores of 300 randomly selected college bound students. (a) What is the class width? How many classes are represented in the graph? (b) What are the lower and upper limits of the first class? (c) What are the lower and upper limits of the last class? (d) Estimate the number of students who had a writing score of 350 or below. (e) Estimate the number of students who had a writing score above 650. (f) In which class did the most students fall? Estimate the number of students in this class. 6

7 (a) What is the class width? How many classes are represented in the graph? (b) What is the midpoint of the first class? What are the lower and upper limits of the first class? (c) What is the midpoint of the last class? What are the lower and upper limits of the last class? (d) Which age group has the highest number of deaths due to legal intervention? Estimate the number of deaths for this age group. (e) Which age group has the lowest number of deaths due to legal intervention? Estimate the number of deaths for this age group. (f) Estimate the relative frequency for the first class. 7

8 4. Draw Time Series Graphs A time series plot is obtained by plotting the time in which a variable is measured on the horizontal axis and the corresponding value of the variable on the vertical axis. 8

9 4. Draw Time Series Graphs The data in the table represent the closing price of Cisco Systems stock at the end of each month from January 2006 through December Construct a time series plot of the data. 4. Draw Time Series Graphs 9