GCSE EDEXCEL Maths- how to draw a frequency polygon?

Question

How do you draw a frequency diagram for the following data;
0-10 (2)
11-20 (5)
21-30 (12)
31-40 (4)
41-50 (5)

Answer 1

Your data appear to be discrete, such as marks in a test out of 50. We will assume here that the data are test marks. Normally, in GCSE Maths, a frequency polygon shows the Frequency on the y-axis plotted against the Mark. Your data are grouped and so the mark used to plot a point is the midpoint value of the group. For example, the midpoint mark of the second group, 11-20, is 15.5, obtained by calculating the mean of the two values, 11 and 20. Therefore, the second group is represented on the graph by a point plotted at mark=15.5 and frequency=5. The next point along (the third group) is plotted similarly at mark=25.5 and frequency =12, and so on.



There is a slight problem with the first group (0-10), but leave that for the moment. As with plotted points on any graph, you should show each point clearly with a cross (× or +). The axes must be clearly labelled (such as Frequency and Mark) and a suitable scale chosen. The x-axis scale can start at 0 with equally spaced divisions as in 0, 10, 20 etc. The frequency axis starts at zero (always) with a scale such as 0, 2, 4, etc, up to 12.



If the first group started at 1 instead of 0, it would be similar to the other groups and contain 10 possible values, 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10. The midpoint of that is 5.5. Because it starts at zero there are 11 possible values and so the midpoint is 5, the mean of 0 and 10. Therefore the first point on the graph is plotted at 5 and not 5.5.



A frequency polygon is a line graph and so to complete the graph you join the plotted points by straight lines. In GCSE Maths there is no need to continue the line of the graph beyond the first and last points.



For an explanation and example graphs of frequency polygons, see pages 11 and 12 of:



http://www.edu-sol.co.uk/histograms/histograms.html



There is a further problem with the first group (0-10) which you may prefer to ignore. Because the group contains 11 possible values and the others contain 10, the first group is wider. If you are doing the higher tier you will know that for groups (classes) with unequal width, you should plot frequency density, not frequency, on a histogram. The same applies to frequency polygons. In AS Maths you would be expected to plot frequency density for a frequency polygon with unequal class widths. See, for example page 17 of this advanced level online book:



http://books.google.co.uk/books?id=Y4IJuQ22nVgC&pg=PA17&lpg=PA17&dq=%22frequency+polygon%22+%22frequency+density%22+&source=web&ots=C1ZkOYtNL1&sig=tEUAHELITox9NVh0KLx8VqtwWLI&hl=en&sa=X&oi=book_result&resnum=2&ct=result



For example, for the second and subsequent groups, the width is 10. The frequency density for the second group is frequency 5 divided by width 10 (5/10) equals 0.5. But for the first group the density is frequency 2 divided by 11 giving approx 0.18. Having calculated the densities you then plot frequency density, not frequency, on the y-axis. This is a complication that you may prefer to ignore and stick with frequency.

Answer 2

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Answer 3

How To Draw Frequency Polygon

Answer 4

A frequency polygon is a line graph of frequency against score. The easiest way is to first draw a histogram, which is a column graph, then join the centres of the columns.



First draw a set of axes. On the horizontal mark the ends of your class intervals i.e. 0, 10, 20, 30 etc



On the vertical put your frequency, from zero up to 12 ( or maybe a little more)



The first class interval 0 - 10 has a frequency of 2, so draw a column up to a frequency of 2. The next class interval, 11 to 20 has a class interval of 5. Draw in this column. Keep going till you have finished the histogram.



To draw the frequency polygon, mark the center of each column then join the dots. Some books bring the polygon down to the axis in the middle of an empty class interval at each end.

Answer 5

gcse edexcel maths draw frequency polygon

Answer 6

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Answer 7

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