The Technology Context – B101

Statistical and graphical summary of data

Academic year 2011/12



Objectives:

1. Practices for using charts
2. Compare the usage of several types of charts
3. Describe data sets using common statistical calculations
4. Some common issues when using statistics

Using graphics in presentations

People tend to remember visual elements in this order.

Using graphics in presentations

Use of colors could be associated with emotions, ideas or cultural values.

	Green: growth, movement
	Blue: calm, institutional
	Purple: spiritual
	Red: power, energy, danger

Diagrams and graphs illustrate data and/or relationships

Line graphs show time and data relationships.

Domestic Material Consumption and GDP (1990 to 2005)

Diagrams and graphs illustrate data and/or relationships

Compare data with bar charts.

Waste by Sector (1998–9 to 2002–3)




Waste Disposal (1998–9 to 2002–3)

Diagrams and graphs illustrate data and/or relationships

Pie charts are useful to show the composition of data.

Diagrams and graphs illustrate data and/or relationships

Diagrams often show scientific relationships.

Periodic Table of Elements

Diagrams and graphs illustrate data and/or relationships

Diagrams often show process relationships.

Flowchart of Nested Decisions

Diagrams and graphs illustrate data and/or relationships

Organisational charts show people relationships.

Suggestions for using charts

• Use a chart title that at least indicates what and when the data was collected.
• Use a scale that is meaningful for the data.
• Use labels that are simple, but sufficiently descriptive, of the data.
• Indicate units of measurements to clarify the data.
• Consider using shapes or arrows to highlight parts of a chart.
• Revise charts as you would revise text.

What are some useful descriptions about this data set?

Percentage of Households with Internet Access at Home (2005)
	National	No children	With children	Rural	Suburban	City
Czech Republic	19	11	33	17	18	22
Finland	54	46	79	51	56	59
Germany	62	56	82	62	61	62
Greece	22	20	27	16	15	29
Ireland	47	41	58	47	49	46
Italy	39	33	51	34	38	41
Netherlands	78	70	92	75	78	80
Spain	36	32	44	23	34	42
Sweden	73	66	89	72	83	67
United Kingdom	60	55	73	67	64	58

There are 10 elements in this data set

Percentage of Households with Internet Access at Home (2005)
	National	No children	With children	Rural	Suburban	City
Czech Republic	19	11	33	17	18	22
Finland	54	46	79	51	56	59
Germany	62	56	82	62	61	62
Greece	22	20	27	16	15	29
Ireland	47	41	58	47	49	46
Italy	39	33	51	34	38	41
Netherlands	78	70	92	75	78	80
Spain	36	32	44	23	34	42
Sweden	73	66	89	72	83	67
United Kingdom	60	55	73	67	64	58

There are 6 variables in this data set

Percentage of Households with Internet Access at Home (2005)
	National	No children	With children	Rural	Suburban	City
Czech Republic	19	11	33	17	18	22
Finland	54	46	79	51	56	59
Germany	62	56	82	62	61	62
Greece	22	20	27	16	15	29
Ireland	47	41	58	47	49	46
Italy	39	33	51	34	38	41
Netherlands	78	70	92	75	78	80
Spain	36	32	44	23	34	42
Sweden	73	66	89	72	83	67
United Kingdom	60	55	73	67	64	58

There are 10 observations in this data set

Percentage of Households with Internet Access at Home (2005)
	National	No children	With children	Rural	Suburban	City
Czech Republic	19	11	33	17	18	22
Finland	54	46	79	51	56	59
Germany	62	56	82	62	61	62
Greece	22	20	27	16	15	29
Ireland	47	41	58	47	49	46
Italy	39	33	51	34	38	41
Netherlands	78	70	92	75	78	80
Spain	36	32	44	23	34	42
Sweden	73	66	89	72	83	67
United Kingdom	60	55	73	67	64	58

There are 60 data values in this data set

Percentage of Households with Internet Access at Home (2005)
	National	No children	With children	Rural	Suburban	City
Czech Republic	19	11	33	17	18	22
Finland	54	46	79	51	56	59
Germany	62	56	82	62	61	62
Greece	22	20	27	16	15	29
Ireland	47	41	58	47	49	46
Italy	39	33	51	34	38	41
Netherlands	78	70	92	75	78	80
Spain	36	32	44	23	34	42
Sweden	73	66	89	72	83	67
United Kingdom	60	55	73	67	64	58

3 types of data values

This data set contains cardinal data values, because they may be ranked and compared in a meaningful way.

In contrast, nominal data values cannot be ranked or compared.

In between are ordinal data values, which may be ranked, but not compared.

Percentage of Households with Internet Access at Home (2005)
	National	No children	With children	Rural	Suburban	City
Czech Republic	19	11	33	17	18	22
Finland	54	46	79	51	56	59
Germany	62	56	82	62	61	62
Greece	22	20	27	16	15	29
Ireland	47	41	58	47	49	46
Italy	39	33	51	34	38	41
Netherlands	78	70	92	75	78	80
Spain	36	32	44	23	34	42
Sweden	73	66	89	72	83	67
United Kingdom	60	55	73	67	64	58

2 types of data sets

This data set contains cross sectional data of households with Internet access at home in 2005.

In contrast, time series data are repeatedly collected for the same variables over multiple points in time.

Percentage of Households with Internet Access at Home (2005)
	National	No children	With children	Rural	Suburban	City
Czech Republic	19	11	33	17	18	22
Finland	54	46	79	51	56	59
Germany	62	56	82	62	61	62
Greece	22	20	27	16	15	29
Ireland	47	41	58	47	49	46
Italy	39	33	51	34	38	41
Netherlands	78	70	92	75	78	80
Spain	36	32	44	23	34	42
Sweden	73	66	89	72	83	67
United Kingdom	60	55	73	67	64	58

Purpose of data collection

This data set contains observational data that were not collected in response to any conditions.

In contrast, experimental data are collected for specific variables to measure responses to controlled conditions.

Percentage of Households with Internet Access at Home (2005)
	National	No children	With children	Rural	Suburban	City
Czech Republic	19	11	33	17	18	22
Finland	54	46	79	51	56	59
Germany	62	56	82	62	61	62
Greece	22	20	27	16	15	29
Ireland	47	41	58	47	49	46
Italy	39	33	51	34	38	41
Netherlands	78	70	92	75	78	80
Spain	36	32	44	23	34	42
Sweden	73	66	89	72	83	67
United Kingdom	60	55	73	67	64	58

Measures of location

For countries in the survey, an average of 62.8 percent of households with children have Internet access at home in 2005.

The average value is the arithmetic mean of all data values for one variable.

Percentage of Households with Internet Access at Home (2005)
	National	No children	With children	Rural	Suburban	City
Greece	22	20	27	16	15	29
Czech Republic	19	11	33	17	18	22
Spain	36	32	44	23	34	42
Italy	39	33	51	34	38	41
Ireland	47	41	58	47	49	46
United Kingdom	60	55	73	67	64	58
Finland	54	46	79	51	56	59
Germany	62	56	82	62	61	62
Sweden	73	66	89	72	83	67
Netherlands	78	70	92	75	78	80

Measures of location

For countries in the survey, the median value is 65.5 percent for households with children that have Internet access at home in 2005.

For data sets with an odd number of elements, the median is the middle data value when all values are arranged from lowest to highest.
For data sets with an even number of elements, the median is the average of the two middle data values when all values are arranged from lowest to highest.

Percentage of Households with Internet Access at Home (2005)
	National	No children	With children	Rural	Suburban	City
Greece	22	20	27	16	15	29
Czech Republic	19	11	33	17	18	22
Spain	36	32	44	23	34	42
Italy	39	33	51	34	38	41
Ireland	47	41	58	47	49	46
United Kingdom	60	55	73	67	64	58
Finland	54	46	79	51	56	59
Germany	62	56	82	62	61	62
Sweden	73	66	89	72	83	67
Netherlands	78	70	92	75	78	80

Measures of location

The mode of a data set is the value that occurs most frequently. If there are two modes, the data set is said to be bimodal. If there are more than two modes, the data set is said to be multimodal.

This data set does not have modal value because all values occur only once per variable.

Percentage of Households with Internet Access at Home (2005)
	National	No children	With children	Rural	Suburban	City
Greece	22	20	27	16	15	29
Czech Republic	19	11	33	17	18	22
Spain	36	32	44	23	34	42
Italy	39	33	51	34	38	41
Ireland	47	41	58	47	49	46
United Kingdom	60	55	73	67	64	58
Finland	54	46	79	51	56	59
Germany	62	56	82	62	61	62
Sweden	73	66	89	72	83	67
Netherlands	78	70	92	75	78	80

Measures of location

The Nth percentile of a data set is a value that is equal to or greater than Nth percent of all values in the data set.

• Arrange the data values from lowest to highest.
• Calculate the index using this formula: index = ( N / 100 ) * ( number of elements)
• If the index is not a whole number, round up. The Nth percentile is the data value found at the position indicated by the index.
• If the index is a whole number, the Nth percentile is the average of the values at the positions indicated by the index and index + 1.

The 50th percentile is the same as the median value, which is 65.5 percent for this data set.

Percentage of Households with Internet Access at Home (2005)
	National	No children	With children	Rural	Suburban	City
Greece	22	20	27	16	15	29
Czech Republic	19	11	33	17	18	22
Spain	36	32	44	23	34	42
Italy	39	33	51	34	38	41
Ireland	47	41	58	47	49	46
United Kingdom	60	55	73	67	64	58
Finland	54	46	79	51	56	59
Germany	62	56	82	62	61	62
Sweden	73	66	89	72	83	67
Netherlands	78	70	92	75	78	80

Measures of variability

The range is quick and easy way to indicate the variations in a data set. It is very sensitive to outlying values.

The range for this data set is 65.

Percentage of Households with Internet Access at Home (2005)
	National	No children	With children	Rural	Suburban	City
Greece	22	20	27	16	15	29
Czech Republic	19	11	33	17	18	22
Spain	36	32	44	23	34	42
Italy	39	33	51	34	38	41
Ireland	47	41	58	47	49	46
United Kingdom	60	55	73	67	64	58
Finland	54	46	79	51	56	59
Germany	62	56	82	62	61	62
Sweden	73	66	89	72	83	67
Netherlands	78	70	92	75	78	80

Measures of variability

Standard deviation is a common, but more complex, method of measuring variability. The formula to calculate standard deviation is slightly different if the data set is a complete population or a sample subset.

The standard deviation is 23.5 percent for households with children that have Internet access at home in 2005.

Percentage of Households with Internet Access at Home (2005)
	National	No children	With children	Rural	Suburban	City
Greece	22	20	27	16	15	29
Czech Republic	19	11	33	17	18	22
Spain	36	32	44	23	34	42
Italy	39	33	51	34	38	41
Ireland	47	41	58	47	49	46
United Kingdom	60	55	73	67	64	58
Finland	54	46	79	51	56	59
Germany	62	56	82	62	61	62
Sweden	73	66	89	72	83	67
Netherlands	78	70	92	75	78	80

Measures of variability

Approximately 68% of data values will be within one standard deviation of the average value.

Percentage of Households with Internet Access at Home (2005)
	National	No children	With children	Rural	Suburban	City
Greece	22	20	27	16	15	29
Czech Republic	19	11	33	17	18	22
Spain	36	32	44	23	34	42
Italy	39	33	51	34	38	41
Ireland	47	41	58	47	49	46
United Kingdom	60	55	73	67	64	58
Finland	54	46	79	51	56	59
Germany	62	56	82	62	61	62
Sweden	73	66	89	72	83	67
Netherlands	78	70	92	75	78	80

Measures of variability

Approximately 95% of data values will be within two standard deviation of the average value.

Percentage of Households with Internet Access at Home (2005)
	National	No children	With children	Rural	Suburban	City
Greece	22	20	27	16	15	29
Czech Republic	19	11	33	17	18	22
Spain	36	32	44	23	34	42
Italy	39	33	51	34	38	41
Ireland	47	41	58	47	49	46
United Kingdom	60	55	73	67	64	58
Finland	54	46	79	51	56	59
Germany	62	56	82	62	61	62
Sweden	73	66	89	72	83	67
Netherlands	78	70	92	75	78	80

Using statistics

The data sample should be representative of the population being measured.

In particular, watch out for data from self-selecting samples.

For example, taking a survey at a football game to find out how many people know the name of the England team captain.

Using statistics

The decision to compare numbers or percentages could have different emphasis.

For example, the score of a football game is Tottenham 2 and Chelsea 1.

We could say, Tottenham scored 1 more than Chelsea, or

... Tottenham scored 100% more than Chelsea.

Using statistics

The use of average or median values may not be useful descriptions of the data set.

	20
	21
	21
Median	22
	22
Average	31
	80

Using statistics

The use of average or median values may not be useful descriptions of the data set.

The median is 110 and the average is 108 for the data set below.

11

25

40

180

190

200

Using statistics

Reverse implication is often false.

For example, households in densely populated areas are more likely to have Internet access at home.

However, not all households with Internet access at home are located in densely populated areas.

Using statistics

Implication is not the same as causation.

For example, households with children are more likely to have Internet access at home.

However, having children does not cause an Internet connection at home.