Variables, Data and Statistics

Question 1

What are variables?

Answer 1

Feature of population which is of interest

Question 2

What kinds of qualitative data are there?

Answer 2

• Nominal
  
  • Eye colour, job
• Ordinal (inherent order)
  
  • Rank teaching as poor/fair/good/verygood
  • Order needs to be preserved
  • Age (18-25, 25-30)

Question 3

What kinds of quantitate data are there?

Answer 3

• Discrete (count)
  
  • Almost every case - whole numbers
  • Number of people
  • Age (as of last birthday)
  • Bar charts
• Continuous (interval)
  
  • Things we’ve measured
  • Height, weight, exam marks, incomes,
  • Age (exact)
  • Histograms
• Ratio data
  
  • Data that have all the characteristics of continuous data but also have a true zero point

Question 4

What is the notation for population average?

Answer 4

µ

Question 5

What is the notation for population variance?

Answer 5

σ2

Question 6

What is the notation for population standard deviation?

Answer 6

σ

Question 7

What is the notation for sample average?

Answer 7

X̅

Question 8

What is the notation for sample variance?

Answer 8

s2

Question 9

What is the notation for sample standard deviation?

Answer 9

s

Question 10

What is the notation for sample correlation?

Answer 10

r

Question 11

What is the notation for sample proportion?

Answer 11

p̂

Question 12

What is the notation for population proportion?

Answer 12

p

Question 13

Which measure of centre is best?

Answer 13

• Mean generally most commonly used but it is sensitive to extreme values
• If data skewed/extreme values present, median better (median is robust to outliers) (real estate prices)
• Mode generally best for categorical data (ratings etc)

Question 14

Describe the mean median relationship

Answer 14

• If symmetric, mean = median
• If positive skew, mean > median
• If negative skew, mean

Question 15

What is the coefficient of variation?

Answer 15

• A measure of spread of data as a proportion of the level of the centre
• Equal to the standard deviation devided by the mean multiplied by 100%
• Called cv
• cv = s/X̅
• Sometime x 100 and reported as a percentage
• Not same units as data
• Especially useful when comparing two or more sets of data that are measured in different units

Question 16

How are percentiles found?

Answer 16

• Location of the Pth percentile = ((number of data points + 1) x P)/100
• Lp = ((n+1)P)/100

Question 17

What is a covariance?

Answer 17

• Measures the strength of the linear relationship between X and Y
• Sign indicates direction of slope (negative vs positive relationship), but magnitude of covariance is dependent on units of measurement (so cannot indicate strength of relationship) - doesn’t tell if big or small

Question 18

Describe what covariance’s tell us

Answer 18

• If cov>0, then as X increases, Y increases; as X decreases, Y decreases
• If cov

Question 19

What is the coefficient of correlation?

Answer 19

• Also measures strength of linear relationship between X & Y
• Is bounded between -1 and +1 - extreme relationship
• If covariance = 0 , correlation = 0 - no linear relationship
• Units cancel out
• Correlation ≠ Causation