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# 4 5b Histograms

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### 4 5b Histograms

1. 1. Histograms Not just another bar graph
2. 2. Bar Graphs and Line Graphs <ul><li>Show trends </li></ul><ul><li>Compares </li></ul><ul><li>Ascending and descending data </li></ul>
3. 3. Histograms <ul><li>Compare data </li></ul><ul><li>Divides data into equal groups </li></ul><ul><li>Shows frequency of data in graph form </li></ul><ul><li>Bars are attached to show no data in-between graph bars </li></ul>
4. 4. Observe <ul><li>How are the graphs alike? </li></ul><ul><li>How do they contrast? </li></ul>
5. 5. Hardware Store <ul><li>Two Bins </li></ul><ul><li>Nuts and Bolts </li></ul><ul><li>All sizes put into one of two bins? </li></ul><ul><li>Histogram </li></ul><ul><ul><li>Puts data into different bins to find what is needed more easily </li></ul></ul><ul><ul><li>data recorded by frequency </li></ul></ul>
6. 6. Data shows many modes <ul><li>1 9 </li></ul><ul><li>2 2 2 5 8 </li></ul><ul><li>3 2 3 3 5 </li></ul><ul><li>4 9 </li></ul><ul><li>5 1 1 3 4 5 6 </li></ul><ul><li>6 1 6 7 7 </li></ul><ul><li>7 1 3 8 </li></ul><ul><li>8 0 </li></ul><ul><li>What is the frequency of this range of numbers? </li></ul>
7. 7. Make a histogram <ul><li>Stem and Leaf </li></ul><ul><li>1 9 </li></ul><ul><li>2 2 2 5 8 </li></ul><ul><li>3 2 3 3 5 </li></ul><ul><li>4 9 </li></ul><ul><li>5 1 1 3 4 5 6 </li></ul><ul><li>6 1 6 7 7 </li></ul><ul><li>7 1 3 8 </li></ul><ul><li>8 0 </li></ul>80 78 73 71 67 67 66 61 56 55 54 53 51 51 49 35 33 33 32 28 25 22 22 19 Data
8. 8. How it looks <ul><li>1 9 </li></ul><ul><li>2 2 2 5 8 </li></ul><ul><li>3 2 3 3 5 </li></ul><ul><li>4 9 </li></ul><ul><li>5 1 1 3 4 5 6 </li></ul><ul><li>6 1 6 7 7 </li></ul><ul><li>7 1 3 8 </li></ul><ul><li>8 0 </li></ul><ul><li>Frequency divided into range groupings of 20 </li></ul>75-94 55-74 35-54 15-34
9. 9. Science Data <ul><li>Density of Unknown Liquid (g/ml) 0.98 0.99 0.81 0.99 1.02 1.16 1.17 0.96 0.98 1.01 1.05 1.00 1.16 1.19 1.02 1.20 1.18 1.43 </li></ul><ul><li>Students measured the density of an unknown liquid.  </li></ul><ul><li>Each group had a clear liquid </li></ul><ul><li>Did they have the same substance?  </li></ul><ul><li>Strictly forbidden to drink any unknown liquid in the science lab </li></ul><ul><li>Rely on their density data. </li></ul>
10. 10. Organize Data <ul><li>Density of Unknown Liquid (g/ml) 0.98 0.99 0.81 0.99 1.02 1.16 1.17 0.96 0.98 1.01 1.05 1.00 1.16 1.19 1.02 1.20 1.18 1.43 </li></ul><ul><li>Stem and leaf plot or </li></ul><ul><li>Low-to-High list </li></ul><ul><li>08 1 </li></ul><ul><li>09 6 8 8 9 9 </li></ul><ul><li>10 0 1 2 2 5 </li></ul><ul><li>11 6 6 7 8 9 </li></ul><ul><li>12 0 </li></ul><ul><li>13 </li></ul><ul><li>3 </li></ul><ul><li>Key 10 | 1 = 1.01 </li></ul>
11. 11. Data for Histogram <ul><li>08 1 </li></ul><ul><li>09 6 8 8 9 9 </li></ul><ul><li>10 0 1 2 2 5 </li></ul><ul><li>11 6 6 7 8 9 </li></ul><ul><li>12 0 </li></ul><ul><li>13 </li></ul><ul><li>14 3 </li></ul><ul><li>Low value 0.81 </li></ul><ul><li>High value 1.43 </li></ul><ul><li>18 samples measured. </li></ul><ul><li>Range </li></ul><ul><ul><li>1.43 – 0.81 = 0.62 </li></ul></ul><ul><li>Divide into five bars </li></ul><ul><ul><li>Use a range of 65 for ease of use </li></ul></ul><ul><ul><li>0.65 ÷ 5 = 0.124 </li></ul></ul>
12. 12. Prepare the data <ul><li>Range of each bar’s data: 0.130 </li></ul><ul><li>Raise the in-between value up to a convenient value, such as 0.15 </li></ul><ul><li>Bar values on the x-axis </li></ul><ul><ul><li>0.80 + .15 = 0.95 </li></ul></ul>
13. 13. Appropriate graph divisions? <ul><li>0.80 – 0.95 </li></ul><ul><li>0.95 – 1.10 </li></ul><ul><li>1.10 – 1.25 </li></ul><ul><li>1.25 – 1.40 </li></ul><ul><li>Above 1.40 </li></ul><ul><li>Adjust to 1.49 for each bar value </li></ul><ul><li>0.80 – 0.94 </li></ul><ul><li>0.95 – 1.09 </li></ul><ul><li>1.10 – 1.24 </li></ul><ul><li>1.25 – 1.39 </li></ul><ul><li>Above 1.39 </li></ul>
14. 14. Count data into groups <ul><li>0.80 – 0.94 </li></ul><ul><li>0.95 – 1.09 </li></ul><ul><li>1.10 – 1.24 </li></ul><ul><li>1.25 – 1.39 </li></ul><ul><li>Above 1.39 </li></ul><ul><li>08 1 </li></ul><ul><li>09 6 8 8 9 9 </li></ul><ul><li>10 0 1 2 2 5 </li></ul><ul><li>11 6 6 7 8 9 </li></ul><ul><li>12 0 </li></ul><ul><li>13 </li></ul><ul><li>3 </li></ul>
15. 15. Count data into groups <ul><li>0.80 – 0.94 </li></ul><ul><li>0.95 – 1.09 </li></ul><ul><li>1.10 – 1.24 </li></ul><ul><li>1.25 – 1.39 </li></ul><ul><li>Above 1.39 </li></ul><ul><li>08 1 </li></ul><ul><li>09 6 8 8 9 9 </li></ul><ul><li>10 0 1 2 2 5 </li></ul><ul><li>11 6 6 7 8 9 </li></ul><ul><li>12 0 </li></ul><ul><li>13 </li></ul><ul><li>14 3 </li></ul>
16. 16. Count data into groups <ul><li>0.80 – 0.94 </li></ul><ul><li>0.95 – 1.09 </li></ul><ul><li>1.10 – 1.24 </li></ul><ul><li>1.25 – 1.39 </li></ul><ul><li>Above 1.39 </li></ul><ul><li>08 1 </li></ul><ul><li>09 6 8 8 9 9 </li></ul><ul><li>10 0 1 2 2 5 </li></ul><ul><li>11 6 6 7 8 9 </li></ul><ul><li>12 0 </li></ul><ul><li>13 </li></ul><ul><li>14 3 </li></ul>
17. 17. Count data into groups <ul><li>0.80 – 0.94 </li></ul><ul><li>0.95 – 1.09 </li></ul><ul><li>1.10 – 1.24 </li></ul><ul><li>1.25 – 1.39 </li></ul><ul><li>Above 1.39 </li></ul><ul><li>08 1 </li></ul><ul><li>09 6 8 8 9 9 </li></ul><ul><li>10 0 1 2 2 5 </li></ul><ul><li>11 6 6 7 8 9 </li></ul><ul><li>12 0 </li></ul><ul><li>13 </li></ul><ul><li>14 3 </li></ul>
18. 18. Count data into groups <ul><li>0.80 – 0.94 </li></ul><ul><li>0.95 – 1.09 </li></ul><ul><li>1.10 – 1.24 </li></ul><ul><li>1.25 – 1.39 </li></ul><ul><li>Above 1.39 </li></ul><ul><li>08 1 </li></ul><ul><li>09 6 8 8 9 9 </li></ul><ul><li>10 0 1 2 2 5 </li></ul><ul><li>11 6 6 7 8 9 </li></ul><ul><li>12 0 </li></ul><ul><li>13 </li></ul><ul><li>14 3 </li></ul>
19. 19. Count data into groups <ul><li>0.80 – 0.94 </li></ul><ul><li>0.95 – 1.09 </li></ul><ul><li>1.10 – 1.24 </li></ul><ul><li>1.25 – 1.39 </li></ul><ul><li>Above 1.39 </li></ul><ul><li>08 1 </li></ul><ul><li>09 6 8 8 9 9 </li></ul><ul><li>10 0 1 2 2 5 </li></ul><ul><li>11 6 6 7 8 9 </li></ul><ul><li>12 0 </li></ul><ul><li>13 </li></ul><ul><li>14 3 </li></ul>Values 1 10 6 0 1
20. 20. Frequency Table <ul><li>0.80 – 0.94 </li></ul><ul><li>0.95 – 1.09 </li></ul><ul><li>1.10 – 1.24 </li></ul><ul><li>1.25 – 1.39 </li></ul><ul><li>Above 1.39 </li></ul><ul><li>1 </li></ul><ul><li>10 </li></ul><ul><li>6 </li></ul><ul><li>0 </li></ul><ul><li>1 </li></ul>
21. 21. Interpret Data Values 1 10 6 0 1 1 10 6 1 Measurements of fluid 1.40 + 1.25-1.39 1.10-1.24 0.95-1.09 0.80-0.94         s         d         i         q         i         l             f       o           #
22. 22. Did You Know? <ul><li>You will see lots of gulls perched on the ground or beach before a storm. </li></ul>