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Histograms 11 October, 2014 A histogram is used instead of a bar chart when the bars have unequal width. This helps to give the graph a more realistic visual impression.

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6 5 4 3 2 1 0 123456789 Time (Hours) Fish Caught TimeFish 0 ≤ t < 14 1 ≤ t < 53 5 ≤ t < 74 Why is the bar chart misleading?

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TimeFish 0 ≤ t < 14 1 ≤ t < 53 5 ≤ t < 74 An angler keeps a record of the number of fish caught. The angler puts this information onto a bar chart.

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6 5 4 3 2 1 0 123456789 Time (Hours) Fish Caught TimeFish 0 ≤ t < 14 1 ≤ t < 53 5 ≤ t < 74 The areas of the bars give a false impression To avoid this problem a histogram is used

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4 3 2 1 123456789 Time (Hours) Frequency Density of Fish Caught TimeFish Freq ÷ Width = FD 0 ≤ t < 14 4 ÷ 1 4 1 ≤ t < 53 3 ÷ 4 ¾ 5 ≤ t < 74 4 ÷ 2 2

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Frequency = Freq. Density x Class Width Freq. Density = Frequency ÷ Width Width = Frequency ÷ Freq. Density F FD W TimeFish 0 ≤ t < 28 2 ≤ t < 64 6 ≤ t < 710 Calculate the frequency densities for the data in this table and draw a histogram for the data Here are the results for another angler’s fishing catch

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