1. Lesson Objective
Understand the difference between a Bar Chart and a Frequency Chart
Be able to draw Frequency Charts using sensible groupings
Extend to look at Frequency Polygons

2. Distance, d, from school in Miles
Draw Bar Charts for both of these sets of data:
Students were asked how many brothers or sisters they had
Students were asked how far from school they lived
Number of Siblings
Number of Students 2 1 5 4 3
Distance, d, from school in Miles
Number of Students
0 ≤ t < 1 5
1≤ t < 3 6
3 ≤ t < 5
5 ≤ t < 10 4
10 ≤ t < 20 2

3. Distance, d, from school in Miles
Draw Bar Charts for both of these sets of data:
Students were asked how many brothers or sisters they had
Students were asked how far from school they lived
Number of Siblings
Number of Students 2 1 5 4 3
Distance, d, from school in Miles
Number of Students
0 ≤ t < 1 5
1≤ t < 3 6
3 ≤ t < 5
5 ≤ t < 10 4
10 ≤ t < 20 2
Frequency
0 ≤ t< ≤ t< ≤ t<5 5≤ t< ≤ t< 20 1 2 3 4 5
Distance in miles
Frequency 6 1 2 3 4 5
Frequency 6 1 2 3 4 5
Number of Siblings

4. Distance, d, from school in Miles
Draw Bar Charts for both of these sets of data:
Students were asked how many brothers or sisters they had
Students were asked how far from school they lived
Number of Siblings
Number of Students 2 1 5 4 3
Distance, d, from school in Miles
Number of Students
0 ≤ t < 1 5
1≤ t < 3 6
3 ≤ t < 5
5 ≤ t < 10 4
10 ≤ t < 20 2
Frequency 1 2 3 4 5
Frequency 6 1 2 3 4 5
Number of Siblings

5. Bar Charts: Used for discrete data or categorical data
Bars are always equal widths
Labels for each bar go under the bar
Frequency Charts: Use for grouped data (usually continuous data)
Widths of the bars shows the widths of the group
The horizontal axis is a continuous scale/number line

6. Why do we group continuous data?
How do we choose the best groupings?

7. Draw a Frequency Chart for this data.
People on a bus route were asked how long they had waited to get on the bus. The times are shown below (in minutes)
Draw a Frequency Chart for this data.
Think carefully about your groupings!

8. Intervals of every 2

9. Interval of 5

10. Interval of 10

11. Mixed Intervals

15. Key points:
Draw a Bar Chart for Discrete Data
Draw a Frequency Chart for continuous data
When grouping data: Look for the smallest and biggest values
Divide the gap between the biggest and
smallest values into roughly equal chunks
(2, 5, 10 etc)
Try to avoid a jagged graph by merging
groups together
Whilst not ideal – it is okay to have
different sized intervals. (This is sometimes
essential to include ‘outliers’)
If you join the midpoints of a frequency chart at the tops of the bars you get a ‘Frequency Polygon’. You can draw this without drawing the bars if asked to do so.

16. Draw a Frequency Polygon for this data.
Pupils at a Primary School in Year 6 were asked how long it took them to journey to school. The results are shown below:
Time in mins, t
Number of Pupils
0 ≤ t < 10 3
10 ≤ t < 15 7
15 ≤ t < 20 8
20 ≤ t < 25 4
30 ≤ t < 40 1 40
Draw a Frequency Polygon for this data.

17. Draw a Frequency Polygon for this data.
Pupils at a Primary School in Year 6 were asked how long it took them to journey to school. The results are shown below:
Time in mins, t
Number of Pupils
0 ≤ t < 10 3
10 ≤ t < 15 7
15 ≤ t < 20 8
20 ≤ t < 25 4
30 ≤ t < 40 1 40
Draw a Frequency Polygon for this data.

18. Lesson Objective
Consolidate knowledge of Frequency Charts
Be able to draw Frequency Polygons
What are the main differences between a Frequency Chart and a Bar Chart?
What is a Frequency Polygon?

19. Key points:
Draw a Bar Chart for Discrete Data
Draw a Frequency Chart for continuous data
When grouping data: Look for the smallest and biggest values
Divide the gap between the biggest and
smallest values into roughly equal chunks
(2, 5, 10 etc)
Try to avoid a jagged graph by merging
groups together
Whilst not ideal – it is okay to have
different sized intervals. (This is sometimes
essential to include ‘outliers’)
If you join the midpoints of a frequency chart at the tops of the bars you get a ‘Frequency Polygon’. You can draw this without drawing the bars if asked to do so.

20. Exam Questions from AQA

21. People are really bad at drawing Frequency Polygons
What is wrong with these frequency polygons?.

22. People are really bad at drawing Frequency Polygons
What is wrong with these frequency polygons?.
Obviously we don’t need the bars but that isn’t the real issue. The scale along the bottom is not continuous (a number line).
This is a Bar Chart and doesn’t have a continuous scale along the x-axis. The data is discrete so a Frequency Polygon is pointless as the data cannot take values between 3 and 4 so showing the shape of the data between 3 and 4 is silly

23. Lesson Objective
Understand the drawbacks of a Frequency Chart for plotting Continuous Data
Be able to alter a Frequency Chart to become a Histogram

24. I observed how long people had to wait (in minutes) to catch the bus at a Park & Ride site. I drew three graphs to illustrate my data. 30 25 20 15 10 5
0 to 1
1 to 5
5 to 10
10 to 20
20 to 40
Frequency
Time (mins)
Frequency
Time (mins) 30 25 20 15 10 5 40

25. Frequency Time (mins) Frequency Time (mins) 30 25 20 15 10 5 0 to 1
0 to 1
1 to 5
5 to 10
10 to 20
20 to 40
Frequency
Time (mins)
Frequency
Time (mins) 30 25 20 15 10 5 40

26. Good: You can easily tell how many people are in each interval. 30 25 20 15 10 5
0 to 1
1 to 5
5 to 10
10 to 20
20 to 40
Frequency
Time (mins)
Good: You can easily tell how many people are in each interval.
Poor: Interval widths look the same even though they are not because the bars are all the same width.
Good: You can quickly see the proportions for each interval; for example around half waited less than 5 mins
Poor: No idea of how many people are actually in each interval.
Frequency
Time (mins) 30 25 20 15 10 5 40
Good: You can easily tell how many people are in each interval. The differing sizes of each interval are obvious.
Poor: The widest bars ‘catch the eye’ and suggest a higher frequency/proportion than they actually have.

27. We like the frequency chart because:
It shows the unequal interval widths clearly
It shows the frequency
BUT What about the proportions?
Frequency
Time (mins) 30 25 20 15 10 5 40

28. ÷ 4 ÷ 5 ÷ 10 ÷ 20 Frequency Time (mins) Frequency Density Time (mins)30 25 20 15 10 5 40
Time (mins)
÷ 4
÷ 5
÷ 10
÷ 20
Frequency
Density 12 10 8 6 4 2 20 30 40 16 14
Time (mins)

29. Actual raw data plotted against time10 20 30 40
Actual raw data plotted against time
Histogram for data
Frequency
Density 12 10 8 6 4 2 20 30 40 16 14
Time (mins)

30. Key Facts About Histograms:
A Histogram is the best type of ‘bar chart’ for continuous data
A Histogram is a Frequency Chart where the heights of each bar have been divided by the width of the bar
The Frequency of each interval in a histogram is therefore the area of the bar not its height. The height is called the Frequency Density.

31. Q 1) Draw a histogram to represent this data:
Time, t, mins
Frequency
0 < t ≤ 5 2
5 < t ≤ 15 6
15 < t ≤ 30 12
30 < t ≤ 60

32. Q 1) Draw a histogram to represent this data: Time, t, mins Frequency
F.D.
0 < t ≤ 5 2
0.4
5 < t ≤ 15 6
0.6
15 < t ≤ 30 12
0.8
30 < t ≤ 60
0.8
0.7
Frequency
Density
0.6
0.5
0.4
0.3
0.2
0.1 10 20 30 40 50 60
Time (mins)

34. Summary: (The four main features)
The heights of the bars now show frequency density. Frequency density is found by dividing the frequency of the interval by the width of the interval
Eg The 1-5 interval had a frequency of 25, so the new height is 25 ÷ 4 = 6.25
The frequency of the interval is now equal to the area of the bar. 12 10 8 6 4 2 20 30 40 16 14
Frequency
Density
Time (mins)
A Histogram is only used for continuous data. It has a continuous scale along the x-axis.
The bars are drawn to show the interval widths.

35. Do the questions:
Everyone should do Question 1.
I would recommend that most of you do Question 2 (as only 1 of you got it right in the test in July), but if you want a challenge try doing questions 3 and 4 instead which are about applying your knowledge backwards.

36. Plenary:
What are the four main features of a histogram?

37. Plenary:
What are the four main features of a histogram?
Continuous scale along the x-axis
Bars are matched to the scale on the x-axis to show interval widths (often different widths)
The area of a bar tells you the frequency, not the height. The heights of the bars are found by dividing the frequency by the interval width.
The vertical axis is labelled frequency density

38. Plenary:
What are the four main features of a histogram?
Continuous scale along the x-axis
Bars are matched to the scale on the x-axis to show interval widths (often different widths)
The area of a bar tells you the frequency, not the height. The heights of the bars are found by dividing the frequency by the interval width.
The vertical axis is labelled frequency density
What do you think the 3/4 marks for each exam question might be awarded for?

40. Extension - Making things easier:
What happens when we work out the frequency densities for these intervals?
1000
2000
3000
4000