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HISTOGRAMS

HISTOGRAMS. Representing Data Module S1. 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 . NO GAPS between Bars. Continuous data.

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HISTOGRAMS

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  1. HISTOGRAMS Representing Data Module S1

  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. NO GAPS between Bars Continuous data

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

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

  6. Grouped Frequency Distribution GAPS! Need to adjust to Continuous Classes No gaps Ready to graph

  7. 4½ 9½ 19½ 29½ 39½ 59½ 5 10 10 10 20 Adjusting Classes Class Widths

  8. Frequency Density

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

  10. 3.0 2.0 1.0 4.5 9.5 19.5 29.5 39.5 49.5 59.5 Freq Dens Time (Mins)

  11. Estimating a Frequency • Imagine we want to Estimate the number of people with a time between 12 and 25 mins • Because rounded to nearest minute • Consider the interval 11.5 to 25.5

  12. Freq Dens 11.5 25.5 3.0 2.0 1.0 4.5 9.5 19.5 29.5 39.5 49.5 59.5 Time (Mins) Frequency = 0.9 x 8 = 7.2 Frequency = 1.8 x 6 = 10.8 Total Frequency = 18

  13. …and the other one? • Simpler to plot • No adjustments required – class widths friendly • No ½ values • Estimation from the EXACT values given • No adjustment required • Estimate 15 to 56 would use 15 and 56! • Appear LESS OFTEN in the exam

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