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

2. HISTOGRAMS AND OGIVES A 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.

3. HISTOGRAMS AND OGIVES The frequency table below represents final grades in an Algebra 2 class. Class LimitsTallyFrequency Class Midpoint Relative Frequency Class Boundaries 50 – 59I154.50.03 60 – 69IIII464.50.11 70 – 79IIIII III874.50.21 80 – 89IIIII IIIII IIIII I1684.50.42 90 - 99IIIII IIII994.50.24

4. HISTOGRAMS AND OGIVES The frequency table below represents final grades in an Algebra 2 class. Class LimitsTallyFrequency Class Midpoint Relative Frequency Class Boundaries 50 – 59I154.50.03 60 – 69IIII464.50.11 70 – 79IIIII III874.50.21 80 – 89IIIII IIIII IIIII I1684.50.42 90 - 99IIIII IIII994.50.24 To create the class boundaries, simply go 0.5 below and above each class limit…

5. HISTOGRAMS AND OGIVES The frequency table below represents final grades in an Algebra 2 class. Class LimitsTallyFrequency Class Midpoint Relative Frequency Class Boundaries 50 – 59I154.50.0349.5 – 59.5 60 – 69IIII464.50.1159.5 – 69.5 70 – 79IIIII III874.50.2169.5 – 79.5 80 – 89IIIII IIIII IIIII I1684.50.4279.5 – 89.5 90 - 99IIIII IIII994.50.2489.5 – 99.5 To create the class boundaries, simply go 0.5 below and above each class limit…

6. HISTOGRAMS AND OGIVES Class LimitsTallyFrequency Class Midpoint Relative Frequency Class Boundaries 50 – 59I154.50.0349.5 – 59.5 60 – 69IIII464.50.1159.5 – 69.5 70 – 79IIIII III874.50.2169.5 – 79.5 80 – 89IIIII IIIII IIIII I1684.50.4279.5 – 89.5 90 - 99IIIII IIII994.50.2489.5 – 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 59.569.5 Grade Averages 79.5 89.5 99.5

7. HISTOGRAMS AND OGIVES Class LimitsTallyFrequency Class Midpoint Relative Frequency Class Boundaries 50 – 59I154.50.0349.5 – 59.5 60 – 69IIII464.50.1159.5 – 69.5 70 – 79IIIII III874.50.2169.5 – 79.5 80 – 89IIIII IIIII IIIII I1684.50.4279.5 – 89.5 90 - 99IIIII IIII994.50.2489.5 – 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 59.569.5 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…

8. HISTOGRAMS AND OGIVES Class LimitsTallyFrequency Class Midpoint Relative Frequency Class Boundaries 50 – 59I 1 54.50.0349.5 – 59.5 60 – 69IIII464.50.1159.5 – 69.5 70 – 79IIIII III874.50.2169.5 – 79.5 80 – 89IIIII IIIII IIIII I1684.50.4279.5 – 89.5 90 - 99IIIII IIII994.50.2489.5 – 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 59.569.5 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

9. HISTOGRAMS AND OGIVES Class LimitsTallyFrequency Class Midpoint Relative Frequency Class Boundaries 50 – 59I154.50.0349.5 – 59.5 60 – 69IIII 4 64.50.1159.5 – 69.5 70 – 79IIIII III874.50.2169.5 – 79.5 80 – 89IIIII IIIII IIIII I1684.50.4279.5 – 89.5 90 - 99IIIII IIII994.50.2489.5 – 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 59.569.5 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

10. HISTOGRAMS AND OGIVES Class LimitsTallyFrequency Class Midpoint Relative Frequency Class Boundaries 50 – 59I154.50.0349.5 – 59.5 60 – 69IIII464.50.1159.5 – 69.5 70 – 79IIIII III 8 74.50.2169.5 – 79.5 80 – 89IIIII IIIII IIIII I1684.50.4279.5 – 89.5 90 - 99IIIII IIII994.50.2489.5 – 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 59.569.5 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 8

11. HISTOGRAMS AND OGIVES Class LimitsTallyFrequency Class Midpoint Relative Frequency Class Boundaries 50 – 59I154.50.0349.5 – 59.5 60 – 69IIII464.50.1159.5 – 69.5 70 – 79IIIII III874.50.2169.5 – 79.5 80 – 89IIIII IIIII IIIII I 16 84.50.4279.5 – 89.5 90 - 99IIIII IIII994.50.2489.5 – 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 59.569.5 Grade Averages 79.5 89.5 99.5 1 4 8 16

12. HISTOGRAMS AND OGIVES Class LimitsTallyFrequency Class Midpoint Relative Frequency Class Boundaries 50 – 59I154.50.0349.5 – 59.5 60 – 69IIII464.50.1159.5 – 69.5 70 – 79IIIII III874.50.2169.5 – 79.5 80 – 89IIIII IIIII IIIII I1684.50.4279.5 – 89.5 90 - 99IIIII IIII 9 94.50.2489.5 – 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 59.569.5 Grade Averages 79.5 89.5 99.5 1 4 8 16 9

13. HISTOGRAMS AND OGIVES Class LimitsTallyFrequency Class Midpoint Relative Frequency Class Boundaries 50 – 59I154.5 0.03 49.5 – 59.5 60 – 69IIII464.5 0.11 59.5 – 69.5 70 – 79IIIII III874.5 0.21 69.5 – 79.5 80 – 89IIIII IIIII IIIII I1684.5 0.42 79.5 – 89.5 90 - 99IIIII IIII994.5 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 59.569.5 Grade Averages 79.5 89.5 99.5.03.42 0.4.10.21 24

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

15. HISTOGRAMS AND OGIVES A 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 BoundariesFrequencyCumulative Frequency 10.5 – 20.523 20.5 – 30.543 30.5 – 40.551 40.5 – 50.527 50.5 – 60.57

16. HISTOGRAMS AND OGIVES A 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 BoundariesFrequencyCumulative Frequency 10.5 – 20.523 20.5 – 30.543 30.5 – 40.551 40.5 – 50.527 50.5 – 60.57

17. HISTOGRAMS AND OGIVES A 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 BoundariesFrequencyCumulative Frequency 10.5 – 20.523 20.5 – 30.543 30.5 – 40.551 40.5 – 50.527 50.5 – 60.57

18. HISTOGRAMS AND OGIVES A 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 BoundariesFrequencyCumulative Frequency 10.5 – 20.523 20.5 – 30.543 30.5 – 40.551 40.5 – 50.527 50.5 – 60.57

19. HISTOGRAMS AND OGIVES A 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 BoundariesFrequencyCumulative Frequency 10.5 – 20.523 20.5 – 30.543 30.5 – 40.551 40.5 – 50.527 50.5 – 60.57

20. HISTOGRAMS AND OGIVES A 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 BoundariesFrequencyCumulative Frequency 10.5 – 20.523 20.5 – 30.543 30.5 – 40.551 40.5 – 50.527 50.5 – 60.57

21. HISTOGRAMS AND OGIVES A 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 BoundariesFrequencyCumulative Frequency 10.5 – 20.523 20.5 – 30.543 30.5 – 40.551 40.5 – 50.527 50.5 – 60.57

22. HISTOGRAMS AND OGIVES An ogive is the graph of the cumulative frequencies… Class BoundariesFrequency Cumulative Frequency 10.5 – 20.523 20.5 – 30.543 30.5 – 40.551 40.5 – 50.527 50.5 – 60.57

23. HISTOGRAMS AND OGIVES An ogive is the graph of the cumulative frequencies… Class BoundariesFrequency Cumulative Frequency 10.5 – 20.523 20.5 – 30.543 30.5 – 40.551 40.5 – 50.527 50.5 – 60.57 Start by setting up your x and y – axis… 10.520.5 30.5 40.5 50.5 60.5 Class Boundaries 40 80 120 160 Cumulative Frequency

24. HISTOGRAMS AND OGIVES An ogive is the graph of the cumulative frequencies… Class BoundariesFrequency Cumulative Frequency 10.5 – 20.523 20.5 – 30.543 30.5 – 40.551 40.5 – 50.527 50.5 – 60.57 Start by setting up your x and y – axis… Place a dot at the smallest class boundary at zero… 10.520.5 30.5 40.5 50.5 60.5 Class Boundaries 40 80 120 160 Cumulative Frequency

25. HISTOGRAMS AND OGIVES An ogive is the graph of the cumulative frequencies… Class BoundariesFrequency Cumulative Frequency 10.5 – 20.523 20.5 – 30.543 30.5 – 40.551 40.5 – 50.527 50.5 – 60.57 Now place dots for each cumulative frequency on the next class boundary 10.520.5 30.5 40.5 50.5 60.5 Class Boundaries 40 80 120 160 Cumulative Frequency

26. HISTOGRAMS AND OGIVES An ogive is the graph of the cumulative frequencies… Class BoundariesFrequency Cumulative Frequency 10.5 – 20.523 20.5 – 30.543 30.5 – 40.551 40.5 – 50.527 50.5 – 60.57 Now place dots for each cumulative frequency on the next class boundary 10.520.5 30.5 40.5 50.5 60.5 Class Boundaries 40 80 120 160 Cumulative Frequency

27. HISTOGRAMS AND OGIVES An ogive is the graph of the cumulative frequencies… Class BoundariesFrequency Cumulative Frequency 10.5 – 20.523 20.5 – 30.543 30.5 – 40.551 40.5 – 50.527 50.5 – 60.57 10.520.5 30.5 40.5 50.5 60.5 Class Boundaries 40 80 120 160 Cumulative Frequency

28. HISTOGRAMS AND OGIVES An ogive is the graph of the cumulative frequencies… Class BoundariesFrequency Cumulative Frequency 10.5 – 20.523 20.5 – 30.543 30.5 – 40.551 40.5 – 50.527 50.5 – 60.57 10.520.5 30.5 40.5 50.5 60.5 Class Boundaries 40 80 120 160 Cumulative Frequency

29. HISTOGRAMS AND OGIVES An ogive is the graph of the cumulative frequencies… Class BoundariesFrequency Cumulative Frequency 10.5 – 20.523 20.5 – 30.543 30.5 – 40.551 40.5 – 50.527 50.5 – 60.57 10.520.5 30.5 40.5 50.5 60.5 Class Boundaries 40 80 120 160 Cumulative Frequency

30. HISTOGRAMS AND OGIVES An ogive is the graph of the cumulative frequencies… Class BoundariesFrequency Cumulative Frequency 10.5 – 20.523 20.5 – 30.543 30.5 – 40.551 40.5 – 50.527 50.5 – 60.57 10.520.5 30.5 40.5 50.5 60.5 Class Boundaries 40 80 120 160 Cumulative Frequency Connect the data points…