CHAPTER 4 FINDING PATTERNS IN DATA: CHARTS & TABLES

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

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

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

Tabulation of Data Person Mode of travel Person Mode of travel   1 car 11 car 2 car 12 bus 3 bus 13 walk 4 car 14 car 5 walk 15 train 6 cycle 16 bus 7 car 17 car 8 cycle 18 cycle 9 bus 19 car 10 train 20 car

Frequency Table Mode of travel Frequency Relative frequency (%) Car 9 45 Bus 4 20 Cycle 3 15 Walk 2 10 Train 2 10 Total 20

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

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

Ungrouped frequency table Number sold Frequency 8 1 9 2 10 6 11 3 12 5 13 3 14 2 More than 14 2 What can we conclude from this table?

Data on length of bolts in mm 49.9 53.8 61.3 45.8 51.2 44.5 55.3 51.4 84.1 55.7 52.7 68.7 52.5 58.8 37.8 44.1 49.9 43.8 64.1 35.9 46.4 45.1 30.6 45.9 54.8 54.0 49.3 46.8 46.5 52.2 33.3 42.9 47.7 46.2 40.5 36.8 47.5 46.3 70.2 35.5 56.7 56.0 56.5 49.5 57.5 52.0 36.8 46.3 42.4 30.2 49.5 36.3 44.6 45.1 30.0 47.0 52.1 53.0 46.1 50.5 56.0 50.9 42.7 42.1 51.2 49.0 49.9 54.4 53.2 43.0 41.3 49.7 42.9 61.1 41.7 35.7 45.0 59.2 60.6 44.7

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

Grouped frequency table of bolt length Interval Frequency Relative frequency (%) 30 to under 35 4 5.00 35 to under 40 7 8.75 40 to under 45 14 17.5 45 to under 50 23 28.75 50 to under 55 16 20.00 55 to under 60 9 11.25 60 to under 65 4 5.00 65 to under 70 1 1.25 70 to under 75 1 1.25 75 to under 80 0 0 80 to under 85 1 1.25 Total 80 100% What does this table tell us?

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

Bar charts Simple bar charts Multiple bar charts Component bar charts Percentage bar charts

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

Simple bar chart of total sales

Multiple bar chart

Component bar chart

Percentage bar chart

Line graph of total sales

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

Bar charts using Excel 2013

Histogram of length of bolt

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

Stem and leaf plot Stem-and-Leaf Display: Length Stem-and-leaf of Length N = 80 Leaf Unit = 1.0 Frequency Stem & Leaf   4.00 3 . 0003 7.00 3 . 5556667 14.00 4 . 01122222334444 23.00 4 . 55555666666677799999999 16.00 5 . 0011122222333444 9.00 5 . 556666789 4.00 6 . 0114 3.00 Extremes (>=68) 3|3 represents 33 mm

Cumulative frequency bolt length Interval F Cumulative F (%) 30 to under 35 4 4 5.00 35 to under 40 7 11 13.75 40 to under 45 14 25 31.25 45 to under 50 23 48 60.00 50 to under 55 16 64 80.00 55 to under 60 9 73 91.25 60 to under 65 4 77 96.25 65 to under 70 1 78 97.50 70 to under 75 1 79 98.75 75 to under 80 0 79 98.75 80 to under 85 1 80 100.0

Cumulative frequency ogive