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Histogram Edexcel S1 Mathematics 2003

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Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.

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Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. (b) Estimate the number of students under 158 cm in height Answer (a): find class boundaries label horizontal axis using continuous scale find class widths find class frequency densities label vertical axis for frequency densities draw bars using class boundaries and frequency densities

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Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. Answer (a): find class boundaries

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Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. Answer (a): find class boundaries Eg boundary between 154 and 155 is 154.5

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Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. Answer (a): find class boundaries Eg boundary between 154 and 155 is 154.5

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Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. Answer (a): find class boundaries Height cm heights of 325 students

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Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. Answer (a): label horizontal axis using continuous scale heights of 325 students Height cm

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Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. Answer (a): label horizontal axis using continuous scale 120130140150160170180190200 Height cm heights of 325 students

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Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. 120130140150160170180190200 Height cm heights of 325 students Answer (a): find class widths

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Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. 120130140150160170180190200 Height cm heights of 325 students Answer (a): find class widths Eg 164.5 – 154.5 = 10

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Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. Answer (a): find class widths 120130140150160170180190200 Height cm heights of 325 students Eg 164.5 – 154.5 = 10

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Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. Answer (a): find class widths 120130140150160170180190200 Height cm heights of 325 students

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Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. 120130140150160170180190200 Height cm heights of 325 students Answer (a): find class frequency densities Frequency density =

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Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. 120130140150160170180190200 Height cm heights of 325 students Answer (a): find class frequency densities Frequency density = Eg=

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Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. Answer (a): find class frequency densities 0 Frequency density (No of students per cm) 120130140150160170180190200 Height cm heights of 325 students Frequency density = Eg= 5

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Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. Answer (a): find class frequency densities 0 Frequency density (No of students per cm) 120130140150160170180190200 Height cm heights of 325 students

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Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. Answer (a): label vertical axis for frequency densities 2 4 0 6 8 10 Frequency density (No of students per cm) 120130140150160170180190200 Height cm 12 heights of 325 students

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Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. Answer (a): draw bars using class boundaries and frequency densities 2 4 0 6 8 10 Frequency density (No of students per cm) 120130140150160170180190200 Height cm 12 heights of 325 students

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Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. Answer (a): draw bars using class boundaries and frequency densities 2 4 0 6 8 10 Frequency density (No of students per cm) 120130140150160170180190200 Height cm 12 heights of 325 students

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Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. Answer (a): draw bars using class boundaries and frequency densities 2 4 0 6 8 10 Frequency density (No of students per cm) 120130140150160170180190200 Height cm 12 heights of 325 students

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Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. Answer (a): draw bars using class boundaries and frequency densities 2 4 0 6 8 10 Frequency density (No of students per cm) 120130140150160170180190200 Height cm 12 heights of 325 students

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Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. Answer (a): draw bars using class boundaries and frequency densities 2 4 0 6 8 10 Frequency density (No of students per cm) 120130140150160170180190200 Height cm 12 heights of 325 students

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Histogram - example Question: The heights of 325 students were measured to the nearest cm (a)Draw a histogram to illustrate the above data. 2 4 0 6 8 10 Frequency density (No of students per cm) 120130140150160170180190200 Height cm 12 Answer (a): draw bars using class boundaries and frequency densities heights of 325 students

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Histogram - example Question: The heights of 325 students were measured to the nearest cm (b) Estimate the number of students under 158 cm in height Answer (b): find class containing 158 2 4 0 6 8 10 Frequency density (No of students per cm) 120130140150160170180190200 Height cm 12 heights of 325 students

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Histogram - example Question: The heights of 325 students were measured to the nearest cm (b) Estimate the number of students under 158 cm in height Answer (b): use interpolation to estimate number under 158 2 4 0 6 8 10 Frequency density (No of students per cm) 120130140150160170180190200 Height cm 12 154.5164.5 5055 50 55 heights of 325 students

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Histogram - example Question: The heights of 325 students were measured to the nearest cm (b) Estimate the number of students under 158 cm in height Answer (b): use interpolation to estimate number under 158 2 4 0 6 8 10 Frequency density (No of students per cm) 120130140150160170180190200 Height cm 12 154.5164.5 5055 heights of 325 students

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Histogram - example Question: The heights of 325 students were measured to the nearest cm (b) Estimate the number of students under 158 cm in height Answer (b): use interpolation to estimate number under 158 2 4 0 6 8 10 Frequency density (No of students per cm) 120130140150160170180190200 Height cm 12 154.5164.5 55 158 heights of 325 students 158 – 154.5 = 3.5 3.5 50

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Histogram - example Question: The heights of 325 students were measured to the nearest cm (b) Estimate the number of students under 158 cm in height Answer (b): use interpolation to estimate number under 158 2 4 0 6 8 10 Frequency density (No of students per cm) 120130140150160170180190200 Height cm 12 154.5164.5 55 158 heights of 325 students 158 – 154.5 = 3.5 50. 10 3.5 50

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Histogram - example Question: The heights of 325 students were measured to the nearest cm (b) Estimate the number of students under 158 cm in height Answer (b): use interpolation to estimate number under 158 2 4 0 6 8 10 Frequency density (No of students per cm) 120130140150160170180190200 Height cm 12 154.5164.5 55 158 heights of 325 students 17.532.5 158 – 154.5 = 3.5 50.= 17.5 10 3.5

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Histogram - example Question: The heights of 325 students were measured to the nearest cm (b) Estimate the number of students under 158 cm in height Answer (b): use interpolation to estimate number under 158 2 4 0 6 8 10 Frequency density (No of students per cm) 120130140150160170180190200 Height cm 12 154.5164.5 55 158 heights of 325 students 17.532.5 158 – 154.5 = 3.5 50.= 17.5 55 + 17.5 = 72.5

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Histogram - example Question: The heights of 325 students were measured to the nearest cm (b) Estimate the number of students under 158 cm in height Answer (b): use interpolation to estimate number under 158 2 4 0 6 8 10 Frequency density (No of students per cm) 120130140150160170180190200 Height cm 12 154.5164.5 55 158 heights of 325 students 158 – 154.5 = 3.5 50.= 12.5 55 + 17.5 = 72.573 students 72.5 Approx 73 students under 158 cm 158 17.532.5

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Histogram - example Question: The heights of 325 students were measured to the nearest cm Answer: 2 4 0 6 8 10 Frequency density (No of students per cm) 120130140150160170180190200 Height cm 12 158 heights of 325 students (a)Draw a histogram to illustrate the above data. (b) Estimate the number of students under 158 cm in height Approx 73 students under 158 cm 72.5

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Step 1: Find the Cumulative Frequency for each class. < 99.5 < 104.5 <109.5 < 114.5 < 119.5 < 124.5 < 129.5 <134.5 0 2 10 28 41 48 49 50.

Step 1: Find the Cumulative Frequency for each class. < 99.5 < 104.5 <109.5 < 114.5 < 119.5 < 124.5 < 129.5 <134.5 0 2 10 28 41 48 49 50.

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