GGR 270 Introductory Analytical Methods 2012
Due Date: November 7th IN CLASS
Organization and presentation should be important considerations in preparing your written assignments. This
includes, but is not necessarily limited to, clearly identifying both questions and answers, including titles and labels for
tables and your answers where appropriate. Your written answers should be clear and concise, not long and drawn
out. Preparing your results in a neat and organized manner is an essential requirement on this and on subsequent
assignments. A penalty of 5% per day will apply to late assignments. Please STAPLE your assignment, and make
sure you have your TA’s name, tutorial section, and time CLEARLY MARKED on your paper.
Question 1. Correlation (40)
You, as a geographer are to explore the relationship between mean annual precipitation (inches of water) and mean
annual temperature (degrees Fahrenheit) in a sample of 9 drainage basins in Southern Ontario. The data associated
with each drainage basin is given in Table 1. Please answer the following questions:
a. Construct a ‘scatter diagram’ for your two variables. Draw the means of both variables on your graph. Comment
briefly on the relationship between the two variables.
b. Compute the “Covariance” and the “Pearson Product Moment Correlation Coefficient”. State the formulae for both
and summarize your work completely in a worktable.
c. Interpret the Covariance and the r value you obtained in (b).
Question 2. Theoretical Distributions and Probability (20)
For Question 2 (a) and (b), draw a small sketch diagram and include it with your answer
a. Assume we have a standard normal distribution
i. What proportion of the curve falls between Z = -0.60 and Z = 1.47
ii. What proportion falls in the range Z ≤ -1.13
b. Now assume we have a normal distribution with a mean of 23.8 and a standard deviation of 7.6. The number of
observations is n=275.
i. What proportion of the observations are expected to fall in the range 17.6 ≤ X ≤ 35.7
ii. How many observations are expected to fall in the range 9.8 ≤ X ≤ 22.0
Question 3. Sampling Methods (20)
Identify both the type (e.g. random, sys