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What is the difference between a cumulative frequency curve & a cumulative frequency polygon?

Dear student,

Please find below the solution to the asked query:

A cumulative frequency graph is a visual representation of ranked categorical data. For example: Grouping people by height categories: under five feet, five feet to six feet, and above six feet. The number of people in each category is the frequency. To find the cumulative frequency, add to each successive category the totals of the lower categories. Graphing these  values taking x as the height and y as the commulative frequency, we get a cumulative frequency graphThis graph is useful  calculating the median of the given data.

To understand commulative frequency polygons, first understand frequcny polygons.Frequency polygons are a graphical device for understanding the shapes of distributions. They serve the same purpose as histograms, but are especially helpful for comparing sets of data. 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.  It will look like this:



A cumulative frequency polygon for the same test scores is shown below. The graph is the same as before except that the y value for each point is the number of students in the corresponding class interval plus all numbers in lower intervals. For example, there are no scores in the interval labeled "35," three in the interval "45," and 10 in the interval "55." Therefore, the y value corresponding to "55" is 13. Since a total of 642 students took the test, the cumulative frequency for the last interval is 642.




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cumulative frequency curve::

An ogive, or cumulative frequency curve, is a type of graph whose y-axis is frequency, from 0 percent to 100 percent, that graphs the cumulative total of the frequencies of each group from one to the next, so it should start at 0, end at 100, and never decrease from one point to the next. 

So if you did a poll of how much each group leaving a grocery store spent, and then marked your x-axis in groups of dollars, say in classes from (0-49) (59-99)(100-149) (150 + +), you would find the percentage of repsonses that fell in each group. If 50 percent fell in the first group, 30 in the second, 5 in the third and 15 in the last group, you get a set of points whose y coordinate would be 50, 80, 85, 100 respectively. 

This type of graph helps you visualize where the biggest jumps in category membership occur. .




cumulative frequency polygon:



A cumulative frequency polygon or ogive is a variation on the frequency polygon. Although both are used to describe a relatively large set of quantitative data, the distinction is that cumulative frequency polygons show cumulative 
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