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Aqa Mod1 Histograms
Aqa Mod1 Histograms
Aqa Mod1 Histograms
Aqa Mod1 Histograms
Aqa Mod1 Histograms
Aqa Mod1 Histograms
Aqa Mod1 Histograms
Aqa Mod1 Histograms
Aqa Mod1 Histograms
Aqa Mod1 Histograms
Aqa Mod1 Histograms
Aqa Mod1 Histograms
Aqa Mod1 Histograms
Aqa Mod1 Histograms
Aqa Mod1 Histograms
Aqa Mod1 Histograms
Aqa Mod1 Histograms
Aqa Mod1 Histograms
Aqa Mod1 Histograms
Aqa Mod1 Histograms
Aqa Mod1 Histograms
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Aqa Mod1 Histograms

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  • 1. Histograms
  • 2. This table shows the height of 50 random secondary school students in the UK Height Frequency 140≤h<150 8 150≤h<155 9 155≤h<160 4 160≤h<165 9 165≤h<170 9 170≤h<185 11 Source: censusatschool.org.uk
  • 3. Drawing a histogram Height Frequency 140≤h<150 8 150≤h<155 9 155≤h<160 4 160≤h<165 9 165≤h<170 9 170≤h<185 11 We need to add a class width column to do this...
  • 4. Drawing a histogram Height Frequency Class width 140≤h<150 8 150≤h<155 9 155≤h<160 4 160≤h<165 9 165≤h<170 9 170≤h<185 11 Like so...
  • 5. Drawing a histogram Giving... Height Frequency Class width 140≤h<150 8 10 150≤h<155 9 5 155≤h<160 4 5 160≤h<165 9 5 165≤h<170 9 5 170≤h<185 11 15
  • 6. To draw a histogram for data with different class widths we need to calculate the frequency density for each class.
  • 7. To calculate frequency density... Frequency Class width
  • 8. Work out the frequency density column... Height Frequency Class width Frequency Density 140≤h<150 8 10 8 ÷ 10 = 0.8 150≤h<155 9 5 155≤h<160 4 5 160≤h<165 9 5 165≤h<170 9 5 170≤h<185 11 15
  • 9. Giving... Height Frequency Class width Frequency Density 140≤h<150 8 10 8 ÷ 10 = 0.8 150≤h<155 9 5 9 ÷ 5 = 1.8 155≤h<160 4 5 4 ÷ 5 = 0.8 160≤h<165 9 5 9 ÷ 5 = 1.8 165≤h<170 9 5 9 ÷ 5 = 1.8 170≤h<185 11 15 11 ÷ 15 = 0.73
  • 10. 185140 145 150 155 160 165 170 175 180 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Height (cm) FrequencyDensity Height Frequency Class width Frequency Density 140≤h<150 8 10 8 ÷ 10 = 0.8 150≤h<155 9 5 9 ÷ 5 = 1.8 155≤h<160 4 5 4 ÷ 5 = 0.8 160≤h<165 9 5 9 ÷ 5 = 1.8 165≤h<170 9 5 9 ÷ 5 = 1.8 170≤h<185 11 15 11 ÷ 15 = 0.73 Now use your values to draw the histogram... remember not to leave any gaps between the bars.
  • 11. Height Frequency Class width Frequency Density 140≤h<150 8 10 8 ÷ 10 = 0.8 150≤h<155 9 5 9 ÷ 5 = 1.8 155≤h<160 4 5 4 ÷ 5 = 0.8 160≤h<165 9 5 9 ÷ 5 = 1.8 165≤h<170 9 5 9 ÷ 5 = 1.8 170≤h<185 11 15 11 ÷ 15 = 0.73 Now use your values to draw the histogram... remember not to leave any gaps between the bars. 185140 145 150 155 160 165 170 175 180 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Height (cm) FrequencyDensity
  • 12. Height Frequency Class width Frequency Density 140≤h<150 8 10 8 ÷ 10 = 0.8 150≤h<155 9 5 9 ÷ 5 = 1.8 155≤h<160 4 5 4 ÷ 5 = 0.8 160≤h<165 9 5 9 ÷ 5 = 1.8 165≤h<170 9 5 9 ÷ 5 = 1.8 170≤h<185 11 15 11 ÷ 15 = 0.73 Now use your values to draw the histogram... remember not to leave any gaps between the bars. 185140 145 150 155 160 165 170 175 180 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Height (cm) FrequencyDensity
  • 13. What, if anything, can we see from this histogram? Why?
  • 14. If we look a bit closer there a few other useful things about a histogram.
  • 15. 140 145 150 155 160 165 170 175 180 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 FrequencyDensity width length For each histogram bar the width is the class width and the length is the frequency density.
  • 16. 140 145 150 155 160 165 170 175 180 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 FrequencyDensity width length With any rectangle if we do width x length we get the area of the rectangle.
  • 17. 140 145 150 155 160 165 170 175 180 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 FrequencyDensity width length And for a histogram the area of the bar is equal to the frequency for that class.
  • 18. How does this work? Frequency Density = Frequency Class width can be rearranged to...
  • 19. Frequency Density = Frequency Class width How does this work? Frequency = Frequency Density × Class width can be rearranged to...
  • 20. Frequency = Frequency Density × Class width width of the bar length of the bar area of the bar
  • 21. KEY POINTS • To draw a histogram for unequal class widths you must calculate frequency density • • The area of a bar on a frequency data histogram is equal to the frequency • Frequency Density = Frequency Class width Frequency = Frequency Density × Class width

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