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# Histograms

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### Histograms

1. 1. Histograms Histograms look like frequency diagrams. The difference is that you get the frequencies from the area of the rectangles and not the height. Frequency Frequency Density Frequency Diagram Histogram
2. 2. Histograms can be used when the class intervals are unequal. Time Frequency 0 < t < 10 20 10 < t < 20 15 20 < t < 30 10 30 < t < 40 9 40 < t < 50 6 Time Frequency 0 < t < 10 20 10 < t < 15 15 15 < t < 20 10 20 < t < 25 9 25 < t < 40 6 Equal Class Intervals Unequal Class Intervals
3. 3. With a histogram you cant not get the frequency from the height of the bar. Instead you get the frequency from the area of the bar. Frequency is equal to the Area of the Bar. Frequency Density is equal to the Height of the Bar. frequency Frequency density = width of interval 0.4 95 110 105 Width of interval = 10 Height (Frequency density) = 0.4 Area (Frequency) = 4
4. 4. Find the relevant information for each bar. 0.5 ? 10 Width of interval = 10 Frequency density = 0.5 Frequency = 5 1.2 ? ? 2 Width of interval = 5 Frequency = 2 Frequency density = 0.4 5 2 8 ? 20 Width of interval = 20 Frequency density = 1.2 Frequency = 24 Frequency = 8 Frequency density = 2 Width of interval = 4
5. 5. Time Frequency 0 < t < 10 20 10 < t < 15 15 15 < t < 20 10 20 < t < 25 9 25 < t < 40 6 Frequency Frequency = Density Class width Frequency Density 2 3 2 1.8 0.4 20 ÷ 10 15 ÷ 5 10 ÷ 5 9÷5 6 ÷ 15 3.0 2.5 Frequency 2.0 Density 1.5 1.0 0.5 0 Time 0 5 10 15 20 25 30 35 40
6. 6. Distance Frequency 0 < t < 20 2 20 < t < 40 4 40 < t < 50 5 50 < t < 70 12 70 < t < 100 9 Frequency Density 0.1 0.2 0.5 0.6 0.3 2 ÷ 20 4 ÷ 20 5 ÷ 10 12 ÷ 20 9 ÷ 30 0.6 0.5 Frequency Density 0.4 0.3 0.2 0.1 0 10 20 30 40 50 Distance 60 70 80 90 100
7. 7. Remember for a histogram the: Frequency is equal to the Area of the bar. Frequency Density is equal to the Height of the bar. 0.5 ? 1.25 ? 0.8 ? 15 8 Area = 15 x 0.5 = 7.5 Area = 1.25 x 8 = 10 20 Area = 20 x 0.8 = 16
8. 8. Copy and complete the table. Frequency = frequency density × width of interval Frequency density 2.4 2.0 Time in seconds 1.6 Frequency Area density × (frequency) width 1.2 95 ≤ t < 105 0.4 × 10 4 0.8 105 ≤ t < 110 1.2 × 5 6 0.4 110 ≤ t < 115 1.4 × 5 7 115 ≤ t < 120 2.2 × 5 11 120 ≤ t < 135 0.4 × 15 6 0 95 100 105 110 115 120 125 130 135 Time in seconds
9. 9. 1.0 0.8 Frequency Density 0.6 0.4 0.2 0 0 20 40 60 80 100 120 Frequency 0 < t < 40 4 40 < t < 80 8 80 < t < 100 16 100 < t < 12 120 120 < t < 12 140 160 Length 200 40 x 0.1 20 x 0.4 20 x 0.8 20 x 1.0 60 x 0.2 180 Distance
10. 10. Graph to compare the distances that males and females travel in the car per week. 50 40 30 20 10 0 Distance 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 Distance 50 40 30 20 10 0
11. 11. Length Frequency 0 < t < 40 40 < t < 80 80 < t < 100 100 < t < 120 120 < t < 200 Length 0 < t < 40 40 < t < 80 80 < t < 100 100 < t < 120 120 < t < 200 Frequency
12. 12. Review Write a definition of each word below. Include methods for calculating. Data set Frequency Class interval Frequency polygon Midpoint Class interval Range Histogram Frequency diagram Frequency density