Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not...
Transcript of Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not...
![Page 1: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/1.jpg)
Histogram
Edexcel S1 Mathematics 2003
![Page 2: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/2.jpg)
Histogram
Used to represent continuous grouped dataDoes not have any gaps between barsAreas represent frequency.
![Page 3: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/3.jpg)
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
![Page 4: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/4.jpg)
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
![Page 5: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/5.jpg)
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
![Page 6: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/6.jpg)
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
![Page 7: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/7.jpg)
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
![Page 8: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/8.jpg)
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
![Page 9: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/9.jpg)
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
![Page 10: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/10.jpg)
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
![Page 11: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/11.jpg)
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
![Page 12: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/12.jpg)
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
![Page 13: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/13.jpg)
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
![Page 14: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/14.jpg)
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
![Page 15: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/15.jpg)
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
![Page 16: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/16.jpg)
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
![Page 17: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/17.jpg)
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
![Page 18: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/18.jpg)
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
![Page 19: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/19.jpg)
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
![Page 20: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/20.jpg)
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
![Page 21: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/21.jpg)
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
![Page 22: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/22.jpg)
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
![Page 23: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/23.jpg)
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
![Page 24: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/24.jpg)
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
![Page 25: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/25.jpg)
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
![Page 26: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/26.jpg)
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
![Page 27: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/27.jpg)
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
![Page 28: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/28.jpg)
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
![Page 29: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/29.jpg)
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
![Page 30: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/30.jpg)
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
![Page 31: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/31.jpg)
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
![Page 32: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/32.jpg)
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
![Page 33: Histogram Edexcel S1 Mathematics 2003. Histogram Used to represent continuous grouped data Does not have any gaps between bars Areas represent frequency.](https://reader035.fdocuments.us/reader035/viewer/2022062619/551606dc550346cf6f8b5e1b/html5/thumbnails/33.jpg)
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