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# Aqa Mod1 Histograms

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Statistics
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• Few things to know about the histogram: http://youtu.be/QR7mHqn14fk

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• Very helpful! I have a Stats test this week and this really cleared things up. Thanks!

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### Transcript

• 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