http://www.ck12.org Chapter 7. Organizing and Displaying Data
TABLE7.18:(continued)
Bin Frequency
[ 20. 5 − 25. 5 ) 4
[ 25. 5 − 30. 5 ) 5
[ 30. 5 − 35. 5 ) 3
[ 35. 5 − 40. 5 ) 2Using this table, construct a frequency polygon.
Step 1:Calculate the midpoint of each bin by adding the 2 numbers of the interval and dividing the sum by 2.
Midpoints:5. 5 + 10. 5
2
=
16
2
= 8
10. 5 + 15. 5
2
=
26
2
= 13
15. 5 + 20. 5
2
=
36
2
= 18
20. 5 + 25. 5
2
=
46
2
= 23
25. 5 + 30. 5
2
=
56
2
= 28
30. 5 + 35. 5
2
=
66
2
= 33
35. 5 + 40. 5
2
=
76
2
= 38
Step 2:Plot the midpoints on a grid, making sure to number thex-axis with a scale that will include the bin sizes.
Join the plotted midpoints with lines.
A frequency polygon usually extends 1 unit below the smallest bin value and 1 unit beyond the greatest bin value.
This extension gives the frequency polygon an appearance of having a starting point and an ending point, which
provides a view of the distribution of data. If the data set were very large so that the number of bins had to be
increased and the bin size decreased, the frequency polygon would appear as a smooth curve.
Example C
The histogram shown below represents the minutes spent practicing per day by a professional violinist for each of
the last 80 days: