1. 8 7 6 5 4 3 2 1
Histograms
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2. How do we present Continuous Data?
Continuous Data can only be presented in groups
We can only present Grouped Continuous Data
The main graph for Grouped Continuous Data is:
A Histogram
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3. Response Times to a Maths Questionf 14 12 10 8 6 4 2
Class interval
(seconds)
Frequency f
0 ≤ t < 10 12
10 ≤ t < 20 14
20 ≤ t < 30 7
30 ≤ t < 40 8
40 ≤ t < 50 5 t
50 ≤ t < 60 4
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4. Response Times to a Maths Questionf 14 12 10 8 6 4 2
A histogram looks like a bar chart but:
Continuous Data means NO GAPS between bars
Histogram
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5. This seems a small difference between a bar chart and a Histogram.
Is that it? NO
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6. The real difference between Bar Charts and Histograms is:
In a Bar Chart the lengths of the bars are proportional to the frequency they represent.
In a Histogram the areas of the rectangles are proportional to the frequency they represent.
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7. Response Times to a Maths Questionf 14 12 10 8 6 4 2
The heights of the bars represent frequency only if the groups are of equal intervals
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8. unequal width intervals
Histograms
with
unequal width intervals
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9. Reaction Times in a Chemistry Experiment
Class interval
(seconds) ?
Frequency
Density
Frequency f
0 ≤ t < 4 3
0.75
Frequency density
4 ≤ t < 5 8 8
5 ≤ t < 6 9 9
Frequency
Density
Frequency =
6 ≤ t < 7 13 13
Class width
7 ≤ t < 8 5 5 t
8 ≤ t < 10 6 3
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10. Reaction Times in a Chemistry Experiment
Class interval
(seconds) 14 12 10 8 6 4 2
Frequency
Density
Frequency f
0 ≤ t < 4 3
0.75
Frequency density
4 ≤ t < 5 8 8
5 ≤ t < 6 9 9
6 ≤ t < 7 13 13
7 ≤ t < 8 5 5 t
8 ≤ t < 10 6 3
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11. Another Example
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12. Lengths of a certain Plant’s Leaves
Class interval
(cm) ?
Frequency
Density
Frequency f
0≤L<4 8 2
Frequency density
4≤L<6 10 5
6≤L<8 12 6
Frequency
Density
Frequency =
8≤L<9 13 13
Class width
9≤L<11 14 7 L
11≤L<15 6
1.5
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13. Lengths of a certain Plant’s Leaves
Class interval
(cm) 14 12 10 8 6 4 2
Frequency
Density
Frequency f
0≤L<4 8 2
Frequency density
4≤L<6 10 5
6≤L<8 12 6
8≤L<9 13 13
9≤L<11 14 7 L
11≤L<15 6
1.5
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14. Exam Question
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15. The area of the rectangles of a histogram represent frequency
The histogram below gives information about the times 120 pupils spent on their last Maths homework.
Use the histogram to complete the frequency table. 5 4 3 2 1
Time
(t min)
Frequency
0 < t ≤ 10 20
The area of the rectangles of a histogram represent frequency
10 < t ≤ 15 25
Frequency density
15 < t ≤ 30 45
30 < t ≤ 60 30
Time, in minutes
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16. Exam Question
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17. Complete the histogram and the frequency table.
The histogram and the table below gives information about the weights of 120 pupils in Year 11
Complete the histogram and the frequency table. 5 4 3 2 1
The area of the rectangles of a histogram represents frequency
Weight
(w kg)
Frequency
30 < w ≤ 40 10
40 < w ≤ 55 45
Frequency density
55 < w ≤ 60 20
60 < w ≤ 90 45
Weight, in kg
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18. © T Madas

19. The area of the rectangles of a histogram represents frequency
The histogram below shows the age distribution of accident and emergency admissions in the Colby City Hospital for a particular month.
Given that there were 90 admissions for the age group, calculate the number of admissions for all the other age groups.
The area of the rectangles of a histogram represents frequency
age
frequency density 30 27 24 21 18 18 15 12 9
225 6
135
225 90
120 5 3 90 45 30
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20. © T Madas

21. The histogram below shows the age distribution of accident and emergency admissions in the Colby City Hospital for a particular month.
Given that there were 90 admissions for the age group, calculate the number of admissions for all the other age groups.
The area of the rectangles of a histogram represents frequency
age
frequency density
Squares :
12 :
4 :
6 :
30 :
18 :
16 :
Data 90 30 45
225
135
120 90
225
135
225 90
120 90 45 30
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22. © T Madas