1. HISTOGRAMS Representing Data OCR Module 9

2. Why use a Histogram When there is a lot of data When data is Continuous a mass, height, volume, time etc Presented in a Grouped Frequency Distribution usually in groups or classes that are UNEQUAL

3. Continuous data NO GAPS between Bars

4. Bars are different in width Determined by Grouped Frequency Distribution

5. AREA is proportional to FREQUENCY NOT height, because of UNEQUAL classes! So we use FREQUENCY DENSITY = Frequency Class width

6. Grouped Frequency Distribution Speed, kph0< v ≤4040< v ≤5050< v ≤6060< v ≤9090< v ≤110 Frequency8015259030 Classes

7. Drawing Sensible Scales Bases correctly aligned Plot the Class Boundaries Heights correct Frequency Density

8. Speed, kph0< v ≤4040< v ≤5050< v ≤6060< v ≤9090< v ≤110 Frequency8015259030 Frequency Density Class width4010 3020 2.01.52.53.01.5 Frequency Densities

9. 040206080100120 3.0 2.0 1.0 Freq Dens Speed (kph) Frequency = Width x Height Frequency = 40 x 2.0 = 80

10. How do we treat ages? Age, Years15 – 1920 – 2425 – 3435 – 3940 - 59 Frequency6020457030 Consider this frequency distribution of the ages of visitors to a department store Class width 5205105 Freq Dens 12 4 4.5 14 1.5 ‘15 – 19’ has an UPPER LIMIT of the 20 th birthday