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Aqa Mod1 Histograms

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    Aqa Mod1 Histograms Aqa Mod1 Histograms Presentation Transcript

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