1. CHAPTER 4
FINDING PATTERNS IN DATA: CHARTS & TABLES

2. Objectives To be able to distinguish between different types of data
To be able to tabulate data into grouped or grouped frequency tables as appropriate
To be able to use diagrams to present data, and to know how to draw appropriate conclusions from these diagrams

3. Types of Data
Ratio - Defined zero can be compared by interval and ratio
Interval - No defined zero
Discrete - Obtained by counting
Ordinal - Has order but intervals between data not meaningful
Nominal – Has no order and little analysis can be done

4. Types of Data cont. How would you define the following sets of data?
Measurements of the weights of jars of coffee
Choice of summer holiday
Weekly earnings
Numbers of students at a university
Market research survey into consumer reaction to a new produce

5. Tabulation of Data Person Mode of travel Person Mode of travel
1 car car
2 car bus
3 bus walk
4 car car
5 walk train
6 cycle bus
7 car car
8 cycle cycle
9 bus car
10 train car

6. Frequency Table Mode of travel Frequency Relative frequency (%)
Car
Bus
Cycle
Walk
Train
Total 20

7. Number of foreign holidays sold
Day No. sold Day No. sold
Monday 10 Monday 13
Tuesday 12 Tuesday 10
Wednesday 9 Wednesday 12
Thursday 10 Thursday 8
Friday 22 Friday 12
Saturday 14 Saturday 12
Monday 11 Monday 11
Tuesday 18 Tuesday 13
Wednesday 10 Wednesday 10
Thursday 10 Thursday 14
Friday 11 Friday 13
Saturday 9 Saturday 12

8. Number of foreign holidays sold cont.
What type of data is this?
What is minimum and maximum?
We will create an ungrouped frequency table

9. Ungrouped frequency table
Number sold Frequency
8 1
9 2
More than
What can we conclude from this table?

10. Data on length of bolts in mm

11. Data on length of bolts in mm cont.
Minimum is 30 mm and maximum is 84.1 mm
We will now group the data into intervals of 5mm (30 to under 35 mm etc). This gives us 11 groups. We can use a tally chart to help us

12. Grouped frequency table of bolt length
Interval Frequency Relative frequency (%)
30 to under
35 to under
40 to under
45 to under
50 to under
55 to under
60 to under
65 to under
70 to under
75 to under
80 to under
Total %
What does this table tell us?

13. Using diagrams to represent data
Pictogram
Pie charts
Bar charts
Histograms
Stem and leaf plots
Line graphs
Frequency polygons
Cumulative frequency ‘ogives’

14. Bar charts Simple bar charts Multiple bar charts Component bar charts
Percentage bar charts

15. Sales of a high street store
Clothing £1.7m £1.4m £1.4m
Furniture £3.4m £4.9m £5.6m
Electrical goods £0.2m £0.4m £0.5m
Total £5.3 m £6.7m £7.5m

16. Simple bar chart of total sales

17. Multiple bar chart

18. Component bar chart

19. Percentage bar chart

20. Line graph of total sales

21. Conclusions
What conclusions can you draw about the sales from these charts?

22. Bar charts using Excel 2013

23. Histogram of length of bolt

24. Properties of a histogram
The area not height is proportional to the frequency
Only used for continuous data
Histograms give an idea of the distribution of the data
Can join up the mid points of a histogram to get a frequency polygon.
Intervals don’t have to be equal but if you change the interval you must adjust the height

25. Stem and leaf plot Stem-and-Leaf Display: Length
Stem-and-leaf of Length N = 80
Leaf Unit = 1.0
Frequency Stem & Leaf
3.00 Extremes (>=68)
3|3 represents 33 mm

26. Cumulative frequency bolt length
Interval F Cumulative F (%)
30 to under
35 to under
40 to under
45 to under
50 to under
55 to under
60 to under
65 to under
70 to under
75 to under
80 to under

27. Cumulative frequency ogive