1. All you’ll ever need to know about histograms…

2. Success Criteria Grade Learning Outcome R A G C2
I can spot the differences between a bar chart and a histogram. C1
I know the difference between continuous and discrete data. B3
I can calculate frequency density from a grouped frequency table. B2
I can draw a histogram correctly, using the frequency density. B1
I can read a histogram, finding the actual number of people in a group using the frequency density. A3
I can draw conclusions from a histogram by performing calculations using information read from that histogram.

3. Spot The Difference Bar Chart Histogram
Write down any differences you notice between the two graphs, including the bars, the axes and note down anything you aren’t sure about.

4. The Differences Bar Chart Histogram Category Property Bars X-Axis
Y-Axis
Category
Property
Bars
X-Axis
Y-Axis

5. The Differences Bar Chart Histogram Category Property Bars
There are gaps between the bars.
X-Axis
Words or categories. (Discrete)
Y-Axis
Number of people or frequency.
Category
Property
Bars
There are no gaps between the bars and they are different widths.
X-Axis
Numbers. (Continuous)
Y-Axis
Frequency density – what’s that?

6. Discrete and Continuous Data – What’s The Difference?
Discrete Data
Continuous Data
Discrete data can not be split up into “bits” – you either watched Eastenders or you didn’t.
Continuous data can be split up – you can have 1.2 metres, 9.87 seconds or be 10.5 years old.
Can you think of any examples of discrete data and continuous data?

7. Success Criteria Grade Learning Outcome R A G C2
I can spot the differences between a bar chart and a histogram. C1
I know the difference between continuous and discrete data. B3
I can calculate frequency density from a grouped frequency table. B2
I can draw a histogram correctly, using the frequency density. B1
I can read a histogram, finding the actual number of people in a group using the frequency density. A3
I can draw conclusions from a histogram by performing calculations using information read from that histogram.

8. Firstly, what does the group 0 ≤ h < 2 mean?
It means:
The group goes from 0 up to 2 hours, including 0 but not including 2.
The group contains any value from 0 up to … hours.

9. Example Of How To Draw A Histogram:
A survey has been conducted on how many hours of TV some children watched last week. Draw a histogram for this data.
Hours (h) spent watching TV last week
Frequency
0 ≤ h < 2 3
2 ≤ h < 5 6
5 ≤ h < 10 10
10 ≤ h < 20 25
20 ≤ h < 40
Why can’t we just plot the frequency?

10. How To Draw A Histogram:
A survey has been conducted on how many hours of TV some children watched last week. Draw a histogram for this data.
Hours (h) spent watching TV last week
Frequency
Frequency Density (Frequency ÷ Group Width)
0 ≤ h < 2 3
3 ÷ 2 = 1.5
2 ≤ h < 5 6
6 ÷ 3 = 2
5 ≤ h < 10 10
10 ÷ 5 = 2
10 ≤ h < 20 25
25 ÷ 10 = 2.5
20 ≤ h < 40
10 ÷ 20 = 0.5
Since the groups are all different widths we need to calculate the frequency density by dividing the frequency by the group width.

11. Drawing the histogram:
Things to notice:
The widths of the bars
are the group widths.
We plot the frequency
density not the
frequency.

12. Drawing the histogram:
How could we calculate the frequency from the graph?
Frequency = Freq. Density x Group Width
Therefore the area of each bar is the frequency.

13. Histogram question:
A survey of the heights of 100 Year 11 students was conducted with the results in the table below. Draw a histogram of this data.
Height (x cm)
Frequency
100 < x ≤ 120 20
120 < x ≤ 140 25
140 < x ≤ 150
150 < x ≤ 160
160 < x ≤ 200 10

14. Answer – first stage: Height (cm) Frequency Frequency Density
100 < x ≤ 120 20
20 ÷ 20 = 1
120 < x ≤ 140 25
25 ÷ 20 = 1.25
140 < x ≤ 150
25 ÷ 10 = 2.5
150 < x ≤ 160
20 ÷ 10 = 2
160 < x ≤ 200 10
10 ÷ 40 = 0.25

15. Answer – second stage: Height (cm) Frequency Frequency Density
100 < x ≤ 120 20 1
120 < x ≤ 140 25
1.25
140 < x ≤ 150
2.5
150 < x ≤ 160 2
160 < x ≤ 200 10
0.25

16. Success Criteria Grade Learning Outcome R A G C2
I can spot the differences between a bar chart and a histogram. C1
I know the difference between continuous and discrete data. B3
I can calculate frequency density from a grouped frequency table. B2
I can draw a histogram correctly, using the frequency density. B1
I can read a histogram, finding the actual number of people in a group using the frequency density. A3
I can draw conclusions from a histogram by performing calculations using information read from that histogram.

17. Reading Histograms
Remember that frequency density is shown on the histogram.
Frequency density = Frequency ÷ Group Width
We discovered earlier that the area of each bar is the frequency.

18. Reading A Histogram
This is a histogram of how many hours of TV some adults watched last week. How many adults were asked in total?

19. Draw yourself a table Hours (h) of TV watched Frequency Density

20. Draw yourself a table Answer: 34 Hours (h) of TV watched
Frequency Density
Frequency
0≤h<5 1 5
5≤h<10 2 10
10≤h<14 8
14≤h<20 6
20≤h<40
0.25
Answer: 34

21. Success Criteria Grade Learning Outcome R A G C2
I can spot the differences between a bar chart and a histogram. C1
I know the difference between continuous and discrete data. B3
I can calculate frequency density from a grouped frequency table. B2
I can draw a histogram correctly, using the frequency density. B1
I can read a histogram, finding the actual number of people in a group using the frequency density. A3
I can draw conclusions from a histogram by performing calculations using information read from that histogram.

22. Drawing Conclusions From Histograms
What percentage of people in the survey below watched 20 hours or more of TV?

23. Calculate how many people are in each group:
What do we do first?
Calculate how many people are in each group:

24. Now find the percentage:

25. Success Criteria Grade Learning Outcome R A G C2
I can spot the differences between a bar chart and a histogram. C1
I know the difference between continuous and discrete data. B3
I can calculate frequency density from a grouped frequency table. B2
I can draw a histogram correctly, using the frequency density. B1
I can read a histogram, finding the actual number of people in a group using the frequency density. A3
I can draw conclusions from a histogram by performing calculations using information read from that histogram.