HISTOGRAMS AND OGIVES A histogram is a visual display of a frequency table. In these graphs we will...

HISTOGRAMS AND OGIVESA histogram is a visual display of a frequency table. In these graphs we will use bars to represent the frequency of each class.

HISTOGRAMS AND OGIVESA histogram is a visual display of a frequency table. In these graphs we will use bars to represent the frequency of each class.

The only new thing we have to figure out is the class boundaries. They are basically 0.5 below and above each classes lower and upper limit.

HISTOGRAMS AND OGIVESThe frequency table below represents final grades in an Algebra 2 class.

Class Limits Tally Frequency Class Midpoint

Relative Frequency

Class Boundaries

50 – 59 I 1 54.5 0.03

60 – 69 IIII 4 64.5 0.11

70 – 79 IIIII III 8 74.5 0.21

80 – 89 IIIII IIIII IIIII I 16 84.5 0.42

90 - 99 IIIII IIII 9 94.5 0.24

HISTOGRAMS AND OGIVESThe frequency table below represents final grades in an Algebra 2 class.

Class Limits Tally Frequency Class Midpoint

Relative Frequency

Class Boundaries

50 – 59 I 1 54.5 0.03

60 – 69 IIII 4 64.5 0.11

70 – 79 IIIII III 8 74.5 0.21

80 – 89 IIIII IIIII IIIII I 16 84.5 0.42

90 - 99 IIIII IIII 9 94.5 0.24

To create the class boundaries, simply go 0.5 below and above each class limit…

HISTOGRAMS AND OGIVESThe frequency table below represents final grades in an Algebra 2 class.

Class Limits Tally Frequency Class Midpoint

Relative Frequency

Class Boundaries

50 – 59 I 1 54.5 0.03 49.5 – 59.5

60 – 69 IIII 4 64.5 0.11 59.5 – 69.5

70 – 79 IIIII III 8 74.5 0.21 69.5 – 79.5

80 – 89 IIIII IIIII IIIII I 16 84.5 0.42 79.5 – 89.5

90 - 99 IIIII IIII 9 94.5 0.24 89.5 – 99.5

To create the class boundaries, simply go 0.5 below and above each class limit…

HISTOGRAMS AND OGIVES

Class Limits Tally Frequency Class Midpoint

Relative Frequency

Class Boundaries

50 – 59 I 1 54.5 0.03 49.5 – 59.5

60 – 69 IIII 4 64.5 0.11 59.5 – 69.5

70 – 79 IIIII III 8 74.5 0.21 69.5 – 79.5

80 – 89 IIIII IIIII IIIII I 16 84.5 0.42 79.5 – 89.5

90 - 99 IIIII IIII 9 94.5 0.24 89.5 – 99.5

Next we create a bar graph with our x – axis as the class boundaries, and the y – axis as the frequency

3

6

9

12

15

18

Frequency

49.5 59.5 69.5

Grade Averages

79.5 89.5 99.5

HISTOGRAMS AND OGIVES

Class Limits Tally Frequency Class Midpoint

Relative Frequency

Class Boundaries

50 – 59 I 1 54.5 0.03 49.5 – 59.5

60 – 69 IIII 4 64.5 0.11 59.5 – 69.5

70 – 79 IIIII III 8 74.5 0.21 69.5 – 79.5

80 – 89 IIIII IIIII IIIII I 16 84.5 0.42 79.5 – 89.5

90 - 99 IIIII IIII 9 94.5 0.24 89.5 – 99.5

Next we create a bar graph with our x – axis as the class boundaries, and the y – axis as the frequency

3

6

9

12

15

18

Frequency

49.5 59.5 69.5

Grade Averages

79.5 89.5 99.5

Now we place bars for each class boundary as high as the frequency found on our table…

HISTOGRAMS AND OGIVES

Class Limits Tally Frequency Class Midpoint

Relative Frequency

Class Boundaries

50 – 59 I 1 54.5 0.03 49.5 – 59.5

60 – 69 IIII 4 64.5 0.11 59.5 – 69.5

70 – 79 IIIII III 8 74.5 0.21 69.5 – 79.5

80 – 89 IIIII IIIII IIIII I 16 84.5 0.42 79.5 – 89.5

90 - 99 IIIII IIII 9 94.5 0.24 89.5 – 99.5

Next we create a bar graph with our x – axis as the class boundaries, and the y – axis as the frequency

3

6

9

12

15

18

Frequency

49.5 59.5 69.5

Grade Averages

79.5 89.5 99.5

Now we place bars for each class boundary as high as the frequency found on our table…

1

HISTOGRAMS AND OGIVES

Class Limits Tally Frequency Class Midpoint

Relative Frequency

Class Boundaries

50 – 59 I 1 54.5 0.03 49.5 – 59.5

60 – 69 IIII 4 64.5 0.11 59.5 – 69.5

70 – 79 IIIII III 8 74.5 0.21 69.5 – 79.5

80 – 89 IIIII IIIII IIIII I 16 84.5 0.42 79.5 – 89.5

90 - 99 IIIII IIII 9 94.5 0.24 89.5 – 99.5

Next we create a bar graph with our x – axis as the class boundaries, and the y – axis as the frequency

3

6

9

12

15

18

Frequency

49.5 59.5 69.5

Grade Averages

79.5 89.5 99.5

Now we place bars for each class boundary as high as the frequency found on our table…

1 4

HISTOGRAMS AND OGIVES

Class Limits Tally Frequency Class Midpoint

Relative Frequency

Class Boundaries

50 – 59 I 1 54.5 0.03 49.5 – 59.5

60 – 69 IIII 4 64.5 0.11 59.5 – 69.5

70 – 79 IIIII III 8 74.5 0.21 69.5 – 79.5

80 – 89 IIIII IIIII IIIII I 16 84.5 0.42 79.5 – 89.5

90 - 99 IIIII IIII 9 94.5 0.24 89.5 – 99.5

Next we create a bar graph with our x – axis as the class boundaries, and the y – axis as the frequency

3

6

9

12

15

18

Frequency

49.5 59.5 69.5

Grade Averages

79.5 89.5 99.5

Now we place bars for each class boundary as high as the frequency found on our table…

1 48

HISTOGRAMS AND OGIVES

Class Limits Tally Frequency Class Midpoint

Relative Frequency

Class Boundaries

50 – 59 I 1 54.5 0.03 49.5 – 59.5

60 – 69 IIII 4 64.5 0.11 59.5 – 69.5

70 – 79 IIIII III 8 74.5 0.21 69.5 – 79.5

80 – 89 IIIII IIIII IIIII I 16 84.5 0.42 79.5 – 89.5

90 - 99 IIIII IIII 9 94.5 0.24 89.5 – 99.5

Next we create a bar graph with our x – axis as the class boundaries, and the y – axis as the frequency

3

6

9

12

15

18

Frequency

49.5 59.5 69.5

Grade Averages

79.5 89.5 99.5

1 48

16

HISTOGRAMS AND OGIVES

Class Limits Tally Frequency Class Midpoint

Relative Frequency

Class Boundaries

50 – 59 I 1 54.5 0.03 49.5 – 59.5

60 – 69 IIII 4 64.5 0.11 59.5 – 69.5

70 – 79 IIIII III 8 74.5 0.21 69.5 – 79.5

80 – 89 IIIII IIIII IIIII I 16 84.5 0.42 79.5 – 89.5

90 - 99 IIIII IIII 9 94.5 0.24 89.5 – 99.5

Next we create a bar graph with our x – axis as the class boundaries, and the y – axis as the frequency

3

6

9

12

15

18

Frequency

49.5 59.5 69.5

Grade Averages

79.5 89.5 99.5

1 48

16

9

HISTOGRAMS AND OGIVES

Class Limits Tally Frequency Class Midpoint

Relative Frequency

Class Boundaries

50 – 59 I 1 54.5 0.03 49.5 – 59.5

60 – 69 IIII 4 64.5 0.11 59.5 – 69.5

70 – 79 IIIII III 8 74.5 0.21 69.5 – 79.5

80 – 89 IIIII IIIII IIIII I 16 84.5 0.42 79.5 – 89.5

90 - 99 IIIII IIII 9 94.5 0.24 89.5 – 99.5

We could change this to a relative frequency histogram by merely changing the y – axis label to relative frequency…

0.1

0.2

0.3

Relative Frequency

49.5 59.5 69.5

Grade Averages

79.5 89.5 99.5

.03

.42

0.4

.10

.21 24

HISTOGRAMS AND OGIVESA cumulative frequency table keeps a running total of the frequencies as you move down the table.

HISTOGRAMS AND OGIVESA cumulative frequency table keeps a running total of the frequencies as you move down the table.

For example, the frequency table shown represents the temperatures (F°) during a season of skiing in Aspen, Colorado.

Class Boundaries Frequency Cumulative Frequency

10.5 – 20.5 23

20.5 – 30.5 43

30.5 – 40.5 51

40.5 – 50.5 27

50.5 – 60.5 7

HISTOGRAMS AND OGIVESA cumulative frequency table keeps a running total of the frequencies as you move down the table.

For example, the frequency table shown represents the temperatures (F°) during a season of skiing in Aspen, Colorado.

The first block of our chart under cumulative frequency will always be the number in the first frequency block…

Class Boundaries Frequency Cumulative Frequency

10.5 – 20.5 23 23

20.5 – 30.5 43

30.5 – 40.5 51

40.5 – 50.5 27

50.5 – 60.5 7

HISTOGRAMS AND OGIVESA cumulative frequency table keeps a running total of the frequencies as you move down the table.

For example, the frequency table shown represents the temperatures (F°) during a season of skiing in Aspen, Colorado.

The first block of our chart under cumulative frequency will always be the number in the first frequency block…

Now we add in each frequency of the next block…

Class Boundaries Frequency Cumulative Frequency

10.5 – 20.5 23 23

20.5 – 30.5 43

30.5 – 40.5 51

40.5 – 50.5 27

50.5 – 60.5 7

HISTOGRAMS AND OGIVESA cumulative frequency table keeps a running total of the frequencies as you move down the table.

For example, the frequency table shown represents the temperatures (F°) during a season of skiing in Aspen, Colorado.

The first block of our chart under cumulative frequency will always be the number in the first frequency block…

Now we add in each frequency of the next block…

Class Boundaries Frequency Cumulative Frequency

10.5 – 20.5 23 23

20.5 – 30.5 43

30.5 – 40.5 51

40.5 – 50.5 27

50.5 – 60.5 7

HISTOGRAMS AND OGIVESA cumulative frequency table keeps a running total of the frequencies as you move down the table.

For example, the frequency table shown represents the temperatures (F°) during a season of skiing in Aspen, Colorado.

The first block of our chart under cumulative frequency will always be the number in the first frequency block…

Now we add in each frequency of the next block…

Class Boundaries Frequency Cumulative Frequency

10.5 – 20.5 23 23

20.5 – 30.5 43

30.5 – 40.5 51

40.5 – 50.5 27

50.5 – 60.5 7

HISTOGRAMS AND OGIVESA cumulative frequency table keeps a running total of the frequencies as you move down the table.

For example, the frequency table shown represents the temperatures (F°) during a season of skiing in Aspen, Colorado.

The first block of our chart under cumulative frequency will always be the number in the first frequency block…

Now we add in each frequency of the next block…

Class Boundaries Frequency Cumulative Frequency

10.5 – 20.5 23 23

20.5 – 30.5 43

30.5 – 40.5 51

40.5 – 50.5 27

50.5 – 60.5 7

HISTOGRAMS AND OGIVESA cumulative frequency table keeps a running total of the frequencies as you move down the table.

For example, the frequency table shown represents the temperatures (F°) during a season of skiing in Aspen, Colorado.

The first block of our chart under cumulative frequency will always be the number in the first frequency block…

Now we add in each frequency of the next block…

Class Boundaries Frequency Cumulative Frequency

10.5 – 20.5 23 23

20.5 – 30.5 43

30.5 – 40.5 51

40.5 – 50.5 27

50.5 – 60.5 7

HISTOGRAMS AND OGIVESAn ogive is the graph of the cumulative frequencies…

Class Boundaries Frequency Cumulative Frequency

10.5 – 20.5 23 23

20.5 – 30.5 43

30.5 – 40.5 51

40.5 – 50.5 27

50.5 – 60.5 7

HISTOGRAMS AND OGIVESAn ogive is the graph of the cumulative frequencies…

Class Boundaries Frequency Cumulative Frequency

10.5 – 20.5 23 23

20.5 – 30.5 43

30.5 – 40.5 51

40.5 – 50.5 27

50.5 – 60.5 7

Start by setting up your x and y – axis… 10.5 20.5 30.5 40.5 50.5 60.5

Class Boundaries

40

80

120

160

Cumulative Frequency

HISTOGRAMS AND OGIVESAn ogive is the graph of the cumulative frequencies…

Class Boundaries Frequency Cumulative Frequency

10.5 – 20.5 23 23

20.5 – 30.5 43

30.5 – 40.5 51

40.5 – 50.5 27

50.5 – 60.5 7

Start by setting up your x and y – axis…

Place a dot at the smallest class boundary at zero…

10.5 20.5 30.5 40.5 50.5 60.5

Class Boundaries

40

80

120

160

Cumulative Frequency

HISTOGRAMS AND OGIVESAn ogive is the graph of the cumulative frequencies…

Class Boundaries Frequency Cumulative Frequency

10.5 – 20.5 23 23

20.5 – 30.5 43

30.5 – 40.5 51

40.5 – 50.5 27

50.5 – 60.5 7

Now place dots for each cumulative frequency on the next class boundary

10.5 20.5 30.5 40.5 50.5 60.5

Class Boundaries

40

80

120

160

Cumulative Frequency

HISTOGRAMS AND OGIVESAn ogive is the graph of the cumulative frequencies…

Class Boundaries Frequency Cumulative Frequency

10.5 – 20.5 23 23

20.5 – 30.5 43

30.5 – 40.5 51

40.5 – 50.5 27

50.5 – 60.5 7

Now place dots for each cumulative frequency on the next class boundary

10.5 20.5 30.5 40.5 50.5 60.5

Class Boundaries

40

80

120

160

Cumulative Frequency

HISTOGRAMS AND OGIVESAn ogive is the graph of the cumulative frequencies…

Class Boundaries Frequency Cumulative Frequency

10.5 – 20.5 23 23

20.5 – 30.5 43

30.5 – 40.5 51

40.5 – 50.5 27

50.5 – 60.5 7

10.5 20.5 30.5 40.5 50.5 60.5

Class Boundaries

40

80

120

160

Cumulative Frequency

HISTOGRAMS AND OGIVESAn ogive is the graph of the cumulative frequencies…

Class Boundaries Frequency Cumulative Frequency

10.5 – 20.5 23 23

20.5 – 30.5 43

30.5 – 40.5 51

40.5 – 50.5 27

50.5 – 60.5 7

10.5 20.5 30.5 40.5 50.5 60.5

Class Boundaries

40

80

120

160

Cumulative Frequency

HISTOGRAMS AND OGIVESAn ogive is the graph of the cumulative frequencies…

Class Boundaries Frequency Cumulative Frequency

10.5 – 20.5 23 23

20.5 – 30.5 43

30.5 – 40.5 51

40.5 – 50.5 27

50.5 – 60.5 7

10.5 20.5 30.5 40.5 50.5 60.5

Class Boundaries

40

80

120

160

Cumulative Frequency

HISTOGRAMS AND OGIVESAn ogive is the graph of the cumulative frequencies…

Class Boundaries Frequency Cumulative Frequency

10.5 – 20.5 23 23

20.5 – 30.5 43

30.5 – 40.5 51

40.5 – 50.5 27

50.5 – 60.5 7

10.5 20.5 30.5 40.5 50.5 60.5

Class Boundaries

40

80

120

160

Cumulative Frequency

Connect the data points…