CHAPTER 4 FINDING PATTERNS IN DATA: CHARTS TABLES

Essential Quantitative Methods 6th Edition

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CHAPTER 4FINDING PATTERNS IN DATA: CHARTS & TABLES


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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


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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


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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


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Tabulation of Data

Person Mode of travel Person Mode of travel 1 car 11 car2 car 12 bus3 bus 13 walk4 car 14 car5 walk 15 train6 cycle 16 bus7 car 17 car8 cycle 18 cycle9 bus 19 car10 train 20 car


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Frequency Table

Mode of travel Frequency Relative frequency (%)

Car 9 45Bus 4 20Cycle 3 15Walk 2 10Train 2 10

Total 20


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Number of foreign holidays sold

Day No. sold Day No. sold

Monday 10 Monday 13Tuesday 12 Tuesday 10Wednesday 9 Wednesday 12Thursday 10 Thursday 8Friday 22 Friday 12Saturday 14 Saturday 12Monday 11 Monday 11Tuesday 18 Tuesday 13Wednesday 10 Wednesday 10Thursday 10 Thursday 14Friday 11 Friday 13Saturday 9 Saturday 12


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• What type of data is this?

• What is minimum and maximum?

• We will create an ungrouped frequency table

Number of foreign holidays sold cont.


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Ungrouped frequency table

Number sold Frequency

8 19 210 611 312 513 314 2More than 14 2

• What can we conclude from this table?


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Data on length of bolts in mm

49.9 53.8 61.3 45.8 51.2 44.5 55.3 51.4 84.155.7 52.7 68.7 52.5 58.8 37.8 44.1 49.9 43.864.1 35.9 46.4 45.1 30.6 45.9 54.8 54.0 49.346.8 46.5 52.2 33.3 42.9 47.7 46.2 40.5 36.847.5 46.3 70.2 35.5 56.7 56.0 56.5 49.5 57.552.0 36.8 46.3 42.4 30.2 49.5 36.3 44.6 45.130.0 47.0 52.1 53.0 46.1 50.5 56.0 50.9 42.742.1 51.2 49.0 49.9 54.4 53.2 43.0 41.3 49.742.9 61.1 41.7 35.7 45.0 59.2 60.6 44.7


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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


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Grouped frequency table of bolt length

Interval Frequency Relative frequency (%)

30 to under 35 4 5.0035 to under 40 7 8.7540 to under 45 14 17.545 to under 50 23 28.7550 to under 55 16 20.0055 to under 60 9 11.2560 to under 65 4 5.0065 to under 70 1 1.2570 to under 75 1 1.2575 to under 80 0 080 to under 85 1 1.25Total 80 100%

• What does this table tell us?


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Using diagrams to represent data

• Pictogram• Pie charts• Bar charts• Histograms• Stem and leaf plots• Line graphs• Frequency polygons• Cumulative frequency ‘ogives’


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Bar charts

• Simple bar charts

• Multiple bar charts

• Component bar charts

• Percentage bar charts


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Sales of a high street store

2012 2013 2014

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


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Simple bar chart of total sales


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Multiple bar chart

0.0

1.0

2.0

3.0

4.0

5.0

6.0

2012 2013 2014

Clothing

Furniture

Electrical goods


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Component bar chart


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Percentage bar chart


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Line graph of total sales


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Conclusions

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


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Bar charts using Excel 2013


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Histogram of length of bolt


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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


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Stem and leaf plot

Stem-and-Leaf Display: Length Stem-and-leaf of Length N = 80Leaf Unit = 1.0

Frequency Stem & Leaf 4.00 3 . 00037.00 3 . 555666714.00 4 . 0112222233444423.00 4 . 5555566666667779999999916.00 5 . 00111222223334449.00 5 . 5566667894.00 6 . 01143.00 Extremes (>=68) 3|3 represents 33 mm


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Cumulative frequency bolt length

Interval F Cumulative F (%)

30 to under 35 4 4 5.0035 to under 40 7 11 13.75 40 to under 45 14 25 31.25 45 to under 50 23 48 60.0050 to under 55 16 64 80.00 55 to under 60 9 73 91.2560 to under 65 4 77 96.25 65 to under 70 1 78 97.5070 to under 75 1 79 98.7575 to under 80 0 79 98.75 80 to under 85 1 80 100.0


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Cumulative frequency ogive

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CHAPTER 4 FINDING PATTERNS IN DATA: CHARTS TABLES