Statistics writing

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FC301E Statistics

Analysing Data

Applications

Module Learning Outcome	Academic Literacy
ML1	AL2
ML2	AL3
ML3	AL5

The lecture notes included in this presentation have been adapted from the resources accompanying the module textbook:

Buglear, J. (2010) Stats Means Business. Oxford: Butterworth Heinemann. eISBN: 9781136435317

Heading

1.1 Bullet point text

1.2

Introduction to theme #

In the first session, we will cover:

XXX

In the second session, we will cover:

XXX

In the third session, we will cover:

XXX

In the fourth session, we will cover:

XXX

The process of analysing data

Step 4

Make conclusions

Suggest further research

Step 3

Summarise findings

Step 2

Mathematical calculations

Graphs and charts

Step 1

Source of data ?

Type of data ?

What do you want to find out ?

Step 1. Comment on the data

What is the source ?

Is the data from a reliable source ?

What type of data is it ?

i.e. Quantitative or Qualitative ?

How was the data collected ?

i.e. by questionnaire, experiment etc

Is the data clear ? Are the units clear ?

What is the question or problem ? i.e. what do you want to find out ?

Step 2. Mathematical calculations

What you want to find out in relation to the data will affect which calculations you carry out and therefore which graphs to use

If there is a reasonable amount of data, measures of central tendency can be calculated

i.e. mean, mode, median, range, standard deviation

The spread of data could be calculated i.e. Minimum, maximum, median, lower and upper quartile

Data could be converted to percentages

Data could be ordered or ranked

Step 2. Graphs and charts

You will not need to use every single type of chart or graph, only those which are relevant and useful

Use…

Stem and Leaf diagram – if you want to present the data in clear groups

Bar chart – if you want to compare a number of factors

Comparative or component bar chart – if you want to compare groups

Pie chart – if you want to represent and compare the relative size of quantities

Step 2. Graphs and charts (continued)

Grouped frequency table – if you want to group data and show frequencies within each group

Histogram – if you want to represent the relative frequencies of a particular factor for a number of groups

Cumulative frequency graph – if you want to represent the cumulative frequencies of each group

Box plots – if you want to represent the 5 point summary of data i.e. Minimum, maximum, median, lower and upper quartile values

Step 2. Charts and Graphs (continued)

Scatter diagram – if you want to represent the relationship between two variables

Regression line (line of best fit)- if you want to represent more specifically just how closely two variables are related

Time series graph – if you want to represent the pattern of data over a period of time

Step 3. Summarise findings

Mathematical calculations can be summarised in table form, in order to make comparisons easier

A short summary can be written about what the mathematical calculations mean in relation to the data

A short summary can be written about the graphs and charts used, to describe what these show in relation to the data

Step 4. Conclusion and further research

A conclusion can be written based on the mathematical calculations and graphical representation of data

Such conclusion are not statistically significant i.e. it can not be argued that the same or similar results would be likely to be found in future or in different situations, without further research and more complex statistical testing

Conclusions will no doubt lead to further questions and ideas for future research.

Now we will look at an example of data

We will follow the 4 steps to analyse the data

We will think about what we could do in each step

In the last seminar this week you will analyse this data in more detail

Example

Population figures (2009)

UK 61.8 million

USA 307 million

Australia 21.9 million

Number of summer Olympics	Number of Gold medals	Number of silver medals	Number of bronze medals	Total number of medals
UK 26	207	255	253	715
USA 25	929	729	638	2296
Australia 24	131	137	164	432
Number of winter Olympics	Number of Gold medals	Number of silver medals	Number of bronze medals	Total number of medals
UK 21	9	3	10	22
USA 21	87	95	71	253
Australia 17	5	1	3	9

Source: Official Olympic website

Source: www.google.co.uk/publicdata

Step 1

The data is quantitative i.e. numerical and measurable

Source of the data are both websites. The official Olympic website would be likely to have accurate and reliable figures. The google data website would be likely to have fairly accurate population figures although more accurate figures would be gained from the individual countries perhaps.

Questions we may want to ask ….

Which country was the most successful at the summer Olympics and which was the most successful at the winter Olympics ?

Is there a difference between summer and winter Olympic number of medals ?

Is there a relationship between population and success at Olympics ?

For each country, what was their most frequent colour of medal ?

Step 2 Mathematical Calculations

Mathematical calculations we may want to carry out on this data include:

Ranking countries in order of success at summer and winter Olympics

Mean number of medals overall (or gold or silver etc)

Range of number of medals overall (or gold or silver etc)

The percentage of gold, silver and bronze medals out of the total number of medals for each country

Step 2 Graphs and Charts

Graphs and charts to visually represent this data could include:

Pie chart showing proportion of gold, silver and bronze medals for each country for summer and winter Olympic games

Pie chart comparing number of medals gained by the three countries

Simple bar charts showing frequency of gold, silver and bronze medals for each country

Comparative bar charts comparing number of medals gained by each country

Scatter diagram to see if or how population figures are related to medal success at the Olympics

Step 3 Summarise findings

From the mean calculations, summarise what the ‘average’ number of medals was and how far above or below average each country was

From the range calculations, summarise which country got the highest number of medals and which country got the lowest and what the difference was

From the percentage calculations, summarise for each country what percentage of gold medals or silver or bronze medals they got out of their total number of medals

Step 3 (continued)

For each bar chart, pie chart etc, summarise what is shown i.e. which country has the highest number of medals, which has the lowest and to describe the difference between them.

For the scatter diagram, to describe the relationship between population and number of medals i.e. was there a positive correlation or negative correlation or no correlation at all ?

Step 4

Based on the summary of the mathematical calculations and the graphs and charts, what conclusions can be reached ?

What further research would be useful ?

E.g. To compare many different countries

E.g. To find out which events each country got their medals in and to study why certain countries are more successful in certain events

E.g. To research the wealth of countries to see if this has an effect on Olympic medal success.

Self study and homework

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