Day 05: STA205 - Introduction to Statistical Methods

• sample mean xbar = 8.37
• median: 8.5
• range: 4
• sample variance s² = 1.83
• sample standard deviation s = 1.35

• A measure of variability is a statistic that describes the spread, or variation, or dispersion in a distribution of data.

• range

  is equal to the largest value in the data minus the smallest value

• sample variance

  • the mean of the squared deviations (differences of individual data value from the mean)
  • Notation - population variance (sigma squared) versus sample variance (s²)
  • Notation, formulas, examples -- sample versus population

• sample standard deviation

  • is calculated as the square root of the sample variance, and represented by s.
  • It is always a non-negative number.
  • It has the same units as the data, and as the mean.
  • Notation:

• We saw that the measures of central tendency cannot distinguish between some amazingly different distributions

• Variability good?
• Variability bad?

This is a rule based on the standard deviation that you'll need to know.

• Based on the standard deviation, which serves as a "typical deviation"
• 68% of the data is within one standard deviation of the mean
• 95% of the data is within two standard deviation of the mean
• 99% of the data is within three standard deviation of the mean
• Works well when the distribution is bell-shaped
• May work okay in any event.
• Example

• exam03-11

• data collection is expensive.
• why collect more than you really need?
• even small samples may be enough: using the Empirical Rule for some self defense:
  • Making an Inference using a sampled observation: p. 93, #1

• Percentages in categories
• Percentages over categories
• Practical Example:
  Problems A, B of Chapter 4 Example
• What do we do with Problem C?

• The definition:
  
• "Z table" (p. 111)
• Deducing/refining the empirical rule
• Using the Z table to do problems:
  Problems C, D, E, F of Chapter 4 Example