They serve the same purpose as histograms, but are especially helpful for comparing sets of data. Frequency polygons are also a good choice for displaying cumulative frequency distributions.
To create a frequency polygon, start just as for histograms , by choosing a class interval. Then draw an X-axis representing the values of the scores in your data. Mark the middle of each class interval with a tick mark, and label it with the middle value represented by the class. Draw the Y-axis to indicate the frequency of each class. Place a point in the middle of each class interval at the height corresponding to its frequency. Finally, connect the points. You should include one class interval below the lowest value in your data and one above the highest value.
The graph will then touch the X-axis on both sides. A frequency polygon for psychology test scores shown in Figure 1 was constructed from the frequency table shown in Table 1.
The first label on the X-axis is This represents an interval extending from Select a suitable class interval for the entire data that is available. Usually, the class interval is plotted on the X- axis or the horizontal line and the frequencies that are corresponding to the class intervals are plotted on the Y- axis or the vertical line.
Once the class mark or the midpoint is chosen for all the class intervals, it becomes very easy to plot the graph. The class mark is represented as follows:. Where U. L is the upper limit and L. L is the lower limit. It is the choice of the person to either mark the class marks or the class intervals on the horizontal axis. The frequencies are also marked on the vertical axis. There are a few important features to note about the frequency polygons.
The height from the horizontal line is always the frequency. It is also important to note that, when the class intervals are being plotted on the X- axis, the midpoint should be considered for the sake of plotting against the frequencies. It should not be plotted against the upper or lower limits. If the class marks are considered directly, then there is nothing to worry about.
The obtained points are joined using the lines and this forms the frequency polygon. Considering the height as the frequency and the width as the class intervals, the bars are drawn on the chart to represent the data as such.
Label the horizontal and vertical axes with words. Include numerical scaling. Construct a frequency polygon from the frequency distribution for the 50 highest ranked countries for depth of hunger.
Find the midpoint for each class. These will be graphed on the x -axis. The frequency values will be graphed on the y -axis values. Use the two frequency tables to compare the life expectancy of men and women from 20 randomly selected countries. Include an overlayed frequency polygon and discuss the shapes of the distributions, the center, the spread, and any outliers. What can we conclude about the life expectancy of women compared to men? Construct a times series graph for a the number of male births, b the number of female births, and c the total number of births.
The following data sets list full time police per , citizens along with homicides per , citizens for the city of Detroit, Michigan during the period from to Suppose that three book publishers were interested in the number of fiction paperbacks adult consumers purchase per month. Each publisher conducted a survey. In the survey, adult consumers were asked the number of fiction paperbacks they had purchased the previous month. The results are as follows:. Often, cruise ships conduct all on-board transactions, with the exception of gambling, on a cashless basis.
At the end of the cruise, guests pay one bill that covers all onboard transactions. Suppose that 60 single travelers and 70 couples were surveyed as to their on-board bills for a seven-day cruise from Los Angeles to the Mexican Riviera.
Following is a summary of the bills for each group. Twenty-five randomly selected students were asked the number of movies they watched the previous week. The results are as follows. Use the following information to answer the next two exercises: Suppose one hundred eleven people who shopped in a special t-shirt store were asked the number of t-shirts they own costing more than? The percentage of people who own at most three t-shirts costing more than?
If the data were collected by asking the first people who entered the store, then the type of sampling is:. Construct a bar graph of obesity rates of your state and the four states closest to your state.
Hint: Label the x -axis with the states. Skip to content Descriptive Statistics. Try It. If necessary, do the same for L2. Into L1, enter 1, 2, 3, 4, 5, 6. Into L2, enter 11, 10, 16, 6, 5, 2. Press 1:Plot1.
Arrow down to TYPE. Arrow to the 3 rd picture histogram. Arrow down to Xlist: Enter L1 2 nd 1. Arrow down to Freq. Enter L2 2 nd 2. Using this data set, construct a histogram. Frequency Polygons Frequency polygons are analogous to line graphs, and just as line graphs make continuous data visually easy to interpret, so too do frequency polygons.
A frequency polygon was constructed from the frequency table below. Age at Inauguration Frequency Constructing a Time Series Graph To construct a time series graph, we must look at both pieces of our paired data set. CO2 Emissions Ukraine United Kingdom United States , , 5,, , , 5,, , , 5,, , , 5,, , , 5,, , , 5,, , , 5,, Uses of a Time Series Graph Time series graphs are important tools in various applications of statistics.
Chapter Review A histogram is a graphic version of a frequency distribution. Answers will vary. One possible histogram is shown:. Construct a frequency polygon for the following: Pulse Rates for Women Frequency 60—69 12 70—79 14 80—89 11 90—99 1 — 1 — 0 — 1 Actual Speed in a 30 MPH Zone Frequency 42—45 25 46—49 14 50—53 7 54—57 3 58—61 1 Tar mg in Nonfiltered Cigarettes Frequency 10—13 1 14—17 0 18—21 15 22—25 7 26—29 2.
Depth of Hunger Frequency — 21 — 13 — 5 — 7 — 1 — 1 — 1. Life Expectancy at Birth — Women Frequency 49—55 3 56—62 3 63—69 1 70—76 3 77—83 8 84—90 2 Life Expectancy at Birth — Men Frequency 49—55 3 56—62 3 63—69 1 70—76 1 77—83 7 84—90 5.
Year Police Which variable increased the fastest? Homework Suppose that three book publishers were interested in the number of fiction paperbacks adult consumers purchase per month. The results are as follows: Publisher A of books Freq. Write them in the charts. For Publishers A and B, make bar widths of one. For Publisher C, make bar widths of two. In complete sentences, give two reasons why the graphs for Publishers A and B are not identical. The figure shows that, although there is some overlap in times, it generally took longer to move the cursor to the small target than to the large one.
It is also possible to plot two cumulative frequency distributions in the same graph. The difference in distributions for the two targets is again evident. Project Leader: David M. Lane, Rice University.
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