Frequency Polygons
FREQUENCY POLYGONS
W H AT I S A F R E Q U E N C Y P O LY G O N
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.
Frequency polygons are also a good choice for displaying cumulative frequency distributions.
H O W T O C R E AT E A F R E Q U E N C Y
P O LY G O N
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.
E X A M P L E O F A F R E Q U E N C Y TA B L E
Lower
Limit
Upper limit Count
Cumulativ e 29.5
39.5
0
0
39.5
49.5
3
3
49.5
59.5
10
13
59.5
69.5
53
66
69.5
79.5
107
173
79.5
89.5
147
320
89.5
99.5
130
450
EXA MP L E OF A FREQ UENCY
P O LY G O N
F R E Q U E N C Y P O LY G O N S F O R
G R O U P E D D ATA
A Frequency Polygon can be uses to represent a frequency distribution with grouped data. The frequency polygon for grouped data is obtained by plotting the frequency against the corresponding mid-point of the class interval and then drawing a straight line in order to join consecutive points
E X A M P L E O F F R E Q U E N C Y P O LY G O N S
G R O U P E D D A TA
Fifty bags of sweets were opened. The number of sweets in each bag is recorded in the following table.
Number of sweets
Frequency
18-22
6
23-27
14
28-32
16
33-37
11
38-42
3
Previous information in frequency polygon form.
DEFINITION OF FREQUENCY
P
W H AT I S A F R E Q U E N C Y P O LY G O N
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.
Frequency polygons are also a good choice for displaying cumulative frequency distributions.
H O W T O C R E AT E A F R E Q U E N C Y
P O LY G O N
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.
E X A M P L E O F A F R E Q U E N C Y TA B L E
Lower
Limit
Upper limit Count
Cumulativ e 29.5
39.5
0
0
39.5
49.5
3
3
49.5
59.5
10
13
59.5
69.5
53
66
69.5
79.5
107
173
79.5
89.5
147
320
89.5
99.5
130
450
EXA MP L E OF A FREQ UENCY
P O LY G O N
F R E Q U E N C Y P O LY G O N S F O R
G R O U P E D D ATA
A Frequency Polygon can be uses to represent a frequency distribution with grouped data. The frequency polygon for grouped data is obtained by plotting the frequency against the corresponding mid-point of the class interval and then drawing a straight line in order to join consecutive points
E X A M P L E O F F R E Q U E N C Y P O LY G O N S
G R O U P E D D A TA
Fifty bags of sweets were opened. The number of sweets in each bag is recorded in the following table.
Number of sweets
Frequency
18-22
6
23-27
14
28-32
16
33-37
11
38-42
3
Previous information in frequency polygon form.
DEFINITION OF FREQUENCY
P