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...
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