Statistics ( investigation report)

Course Work 2:Start 13thApril HAND IN to TURNITIN 8th May 2015 and provide a hard copy to your tutor

You have to produce aninvestigation report consisting of 3 Sections and some OPTIONAL extension work. There should be a maximum number of600 words in total for sections 1-3 and a maximum of 300 words for the extension work. Graphs and charts, which should be included in an appendix, are not included in the word count.

You must answer all the questions in Sections 1 – 3, producing the appropriate diagrams and statistics using either Autograph or Excel.

The data regarding the two indexes are given in Course Work Semester 2 Excel file on Moodle.

These indexes are intended to measure ‘well-being’ of a country.

One index is called “The Happy Planet Index” (HPI)

The other index is called “The Human Development Index” (HDI) (See Note A below for a brief summary describing these indexes)

Section (1)
For each of these two indexes (SEPARATELY)you need to do the following:
  • Examine the distribution of the data by constructing a histogram (You will first need to group the data into suitable intervals and construct a suitable table). You must comment on the shape of the distribution.
  • Find the mean, the median and the interquartile range for each index. (you should be able to get the software package to do this for you – you don’t have to calculate them manually). Comment on how these statistics relate to the shape of the distribution as discussed in (i) above.
  • Use the two indexes to form a scatter diagram.
  • Comment on whether any relationship between the two indexes is apparent from the scatter diagram.
  • By eye, identify any apparent outliers.
  • Find the value of the product moment correlation coefficient.   Comment on the value which you obtain.



Section (2)
Examining the relationship between the measures of Ecological Footprint and Gross Domestic Product (GDP):
  • Draw a scatter diagram with GDP on the horizontal axis and Ecological Footprint on the vertical axis. Find the value of the correlation coefficient
  • Comment on any noticeable features of your graph and the correlation coefficient.
  • Find a line of best fit and interpret this line in terms of the measurements to which it relates.
  • By eye, identify any apparent outliers on the graph.
Section (3)
Looking at some data which may be related to “well-being” :
  • Copy and complete the table below showing the correlation coefficients between pairs of variables:

Table of correlations

Variable GDP Ecological Footprint Well-being Life Expectancy

  • Comment on the correlations found in the table above in part (i) and in particular in relation to the information given in note A below regarding how these indexes are constructed.


NOTE A::These indexes were created by two different organisations.

The HDI is constructed from measurements on life expectancy, educational attainment and income and is expressed as a value between 0 and 1.

The HPI is formed from three component measures on life expectancy, experienced well-being and Ecological Footprint


Looking back at Section 1, consider how those two indexes were formed. Explain whether or not you think they are appropriate ways of measuring well-being / human development?

Try to create your own index. Explain which measures / variables you have used to create this index.

Discuss how your index compares to the other two indexes given in section 1.


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