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Histogram
Edexcel S1 Mathematics 2003
Histogram
Used to represent continuous grouped dataDoes not have any gaps between barsAreas represent frequency.
Histogram - exampleQuestion: 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
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Histogram - exampleQuestion: The heights of 325 students were measured to the nearest cm
(a) Draw a histogram to illustrate the above data.
Height (cm) 130 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Answer (a): find class boundaries
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Histogram - exampleQuestion: The heights of 325 students were measured to the nearest cm
(a) Draw a histogram to illustrate the above data.
Height (cm) 130 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Answer (a): find class boundaries Eg boundary between 154 and 155 is 154.5
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Histogram - exampleQuestion: 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
Boundaries 154.5
Height (cm) 130 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Eg boundary between 154 and 155 is 154.5
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Histogram - exampleQuestion: 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
Boundaries 129.5 154.5 164.5 169.5 179.5 199.5
Height (cm) 130 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Height cm
heights of 325 students
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Histogram - exampleQuestion: 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
Boundaries 129.5 154.5 164.5 169.5 179.5 199.5
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
heights of 325 students
Height cm
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Histogram - exampleQuestion: 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
Boundaries 129.5 154.5 164.5 169.5 179.5 199.5
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
120 130 140 150 160 170 180 190 200Height cm
heights of 325 students
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Histogram - exampleQuestion: The heights of 325 students were measured to the nearest cm
(a) Draw a histogram to illustrate the above data.
Boundaries 129.5 154.5 164.5 169.5 179.5 199.5
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
120 130 140 150 160 170 180 190 200Height cm
heights of 325 students
Answer (a): find class widths
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Histogram - exampleQuestion: The heights of 325 students were measured to the nearest cm
(a) Draw a histogram to illustrate the above data.
Boundaries 129.5 154.5 164.5 169.5 179.5 199.5
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
120 130 140 150 160 170 180 190 200Height cm
heights of 325 students
Answer (a): find class widths Eg 164.5 – 154.5 = 10
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Histogram - exampleQuestion: 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
Widths 10
Boundaries 129.5 154.5 164.5 169.5 179.5 199.5
Height (cm) 130 – 154 155 - 164 165 - 169 170 - 179 180 – 199
Frequency 55 50 60 100 60
120 130 140 150 160 170 180 190 200Height cm
heights of 325 students
Eg 164.5 – 154.5 = 10
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Histogram - exampleQuestion: 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
Widths 25 10 5 10 20
Boundaries 129.5 154.5 164.5 169.5 179.5 199.5
Height (cm) 130 – 154 155 - 164 165 - 169 170 - 179 180 – 199
Frequency 55 50 60 100 60
120 130 140 150 160 170 180 190 200Height cm
heights of 325 students
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Histogram - exampleQuestion: The heights of 325 students were measured to the nearest cm
(a) Draw a histogram to illustrate the above data.
Widths 25 10 5 10 20
Boundaries 129.5 154.5 164.5 169.5 179.5 199.5
Height (cm) 130 – 154 155 - 164 165 - 169 170 - 179 180 – 199
Frequency 55 50 60 100 60
120 130 140 150 160 170 180 190 200Height cm
heights of 325 students
Answer (a): find class frequency densities
Frequency density = widthclass
frequencyclass
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Histogram - exampleQuestion: The heights of 325 students were measured to the nearest cm
(a) Draw a histogram to illustrate the above data.
Widths 25 10 5 10 20
Boundaries 129.5 154.5 164.5 169.5 179.5 199.5
Height (cm) 130 – 154 155 - 164 165 - 169 170 - 179 180 – 199
Frequency 55 50 60 100 60
120 130 140 150 160 170 180 190 200Height cm
heights of 325 students
Answer (a): find class frequency densities
Frequency density = widthclass
frequencyclass
Eg
10
50 =
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Histogram - exampleQuestion: 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
Widths 25 10 5 10 20
Boundaries 129.5 154.5 164.5 169.5 179.5 199.5
Height (cm) 130 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Freq. den 5
0
Frequency
density
(No of students per cm)
120 130 140 150 160 170 180 190 200Height cm
heights of 325 studentsFrequency density =
widthclass
frequencyclass
Eg
10
50 = 5
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Histogram - exampleQuestion: 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
Widths 25 10 5 10 20
Boundaries 129.5 154.5 164.5 169.5 179.5 199.5
Height (cm) 130 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Freq. den 2.2 5 12 10 3
0
Frequency
density
(No of students per cm)
120 130 140 150 160 170 180 190 200Height cm
heights of 325 students
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Histogram - exampleQuestion: 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
Widths 25 10 5 10 20
Boundaries 129.5 154.5 164.5 169.5 179.5 199.5
Height (cm) 130 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Freq. den 2.2 5 12 10 3
2
4
0
6
8
10Frequency
density
(No of students per cm)
120 130 140 150 160 170 180 190 200Height cm
12 heights of 325 students
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Histogram - exampleQuestion: 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
Widths 25 10 5 10 20
Boundaries 129.5 154.5 164.5 169.5 179.5 199.5
Height (cm) 130 – 154 155 - 164 165 - 169 170 - 179 180 – 199
Frequency 55 50 60 100 60
Freq. den 2.2 5 12 10 3
2
4
0
6
8
10Frequency
density
(No of students per cm)
120 130 140 150 160 170 180 190 200Height cm
12 heights of 325 students
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Histogram - exampleQuestion: 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
Widths 25 10 5 10 20
Boundaries 129.5 154.5 164.5 169.5 179.5 199.5
Height (cm) 130 – 154 155 - 164 165 - 169 170 - 179 180 – 199
Frequency 55 50 60 100 60
Freq. den 2.2 5 12 10 3
2
4
0
6
8
10Frequency
density
(No of students per cm)
120 130 140 150 160 170 180 190 200Height cm
12 heights of 325 students
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Histogram - exampleQuestion: 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
Widths 25 10 5 10 20
Boundaries 129.5 154.5 164.5 169.5 179.5 199.5
Height (cm) 130 – 154 155 - 164 165 - 169 170 - 179 180 – 199
Frequency 55 50 60 100 60
Freq. den 2.2 5 12 10 3
2
4
0
6
8
10Frequency
density
(No of students per cm)
120 130 140 150 160 170 180 190 200Height cm
12 heights of 325 students
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Histogram - exampleQuestion: 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
Widths 25 10 5 10 20
Boundaries 129.5 154.5 164.5 169.5 179.5 199.5
Height (cm) 130 – 154 155 - 164 165 - 169 170 - 179 180 – 199
Frequency 55 50 60 100 60
Freq. den 2.2 5 12 10 3
2
4
0
6
8
10Frequency
density
(No of students per cm)
120 130 140 150 160 170 180 190 200Height cm
12 heights of 325 students
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Histogram - exampleQuestion: 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
Widths 25 10 5 10 20
Boundaries 129.5 154.5 164.5 169.5 179.5 199.5
Height (cm) 130 – 154 155 - 164 165 - 169 170 - 179 180 – 199
Frequency 55 50 60 100 60
Freq. den 2.2 5 12 10 3
2
4
0
6
8
10Frequency
density
(No of students per cm)
120 130 140 150 160 170 180 190 200Height cm
12 heights of 325 students
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Histogram - exampleQuestion: The heights of 325 students were measured to the nearest cm
(a) Draw a histogram to illustrate the above data.
Widths 25 10 5 10 20
Boundaries 129.5 154.5 164.5 169.5 179.5 199.5
Height (cm) 130 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Freq. den 2.2 5 12 10 3
2
4
0
6
8
10Frequency
density
(No of students per cm)
120 130 140 150 160 170 180 190 200Height cm
12
Answer (a): draw bars using class boundaries and frequency densities
heights of 325 students
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Histogram - exampleQuestion: 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
10Frequency
density
(No of students per cm)
120 130 140 150 160 170 180 190 200Height cm
12 heights of 325 students
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Histogram - exampleQuestion: 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
10Frequency
density
(No of students per cm)
120 130 140 150 160 170 180 190 200Height cm
12 154.5 164.5
5055
5055
heights of 325 students
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Histogram - exampleQuestion: 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
10Frequency
density
(No of students per cm)
120 130 140 150 160 170 180 190 200Height cm
12 154.5 164.5
5055
heights of 325 students
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Histogram - exampleQuestion: 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
10Frequency
density
(No of students per cm)
120 130 140 150 160 170 180 190 200Height cm
12 154.5 164.5
55
158
heights of 325 students
158 – 154.5 = 3.5
3.5
50
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Histogram - exampleQuestion: 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
10Frequency
density
(No of students per cm)
120 130 140 150 160 170 180 190 200Height cm
12 154.5 164.5
55
158
heights of 325 students
158 – 154.5 = 3.5
50 . 10
5.3
10 3.5
50
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Histogram - exampleQuestion: 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
10Frequency
density
(No of students per cm)
120 130 140 150 160 170 180 190 200Height cm
12 154.5 164.5
55
158
heights of 325 students
17.5 32.5
158 – 154.5 = 3.5
50 . 10
5.3 = 17.5
10 3.5
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Histogram - exampleQuestion: 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
10Frequency
density
(No of students per cm)
120 130 140 150 160 170 180 190 200Height cm
12 154.5 164.5
55
158
heights of 325 students
17.5 32.5
158 – 154.5 = 3.5
50 . 10
5.3 = 17.5
55 + 17.5 = 72.5
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Histogram - exampleQuestion: 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
10Frequency
density
(No of students per cm)
120 130 140 150 160 170 180 190 200Height cm
12 154.5 164.5
55
158
heights of 325 students
158 – 154.5 = 3.5
50 . 10
5.3 = 12.5
55 + 17.5 = 72.5 73 students
72.5
Approx 73 students under 158 cm
158
17.5 32.5
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
Histogram - exampleQuestion: The heights of 325 students were measured to the nearest cm
Answer:
2
4
0
6
8
10Frequency
density
(No of students per cm)
120 130 140 150 160 170 180 190 200Height cm
12
158
heights of 325 students
Widths 25 10 5 10 20
Boundaries 129.5 154.5 164.5 169.5 179.5 199.5
Height (cm) 130 – 154 155 - 164 165 - 169 170 - 179 180 – 199
Frequency 55 50 60 100 60
Freq. den 2.2 5 12 10 3
(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
Height (cm) 13 0 – 154 155 - 164 165 - 169 170 - 179 180 - 199
Frequency 55 50 60 100 60
![Histogram [Www.nikonians.org]](https://img.pdfslide.us/doc/110x75/577cd8911a28ab9e78a17d60/histogram-wwwnikoniansorg.jpg)
