Quantitative Data part 2

Standard Deviation and Variation
  • Population parameter:

  Mean: µ (mew)

  Standard deviation: σ (sigma)

  Variance: σ^2

  • Sample statistic

  Mean: x̄ (x bar)

  Standard deviation: s

  Variance: s^2

  • Standard deviation: typical distance between mean and values in a distribution

  • If a value is less than the mean is added to the data set, the distribution decreases

  • Once observations become more spread out, SD (standard deviation) increases

  • Either 0 or any positive number

  • Not resistant to outliers

  • Standard deviation: units

  • Variation: units^2

Interquartile Range (IQR)
Percentile
  • The pth percentile is defined as the value that P percent of values are less than or equal to it
Quartiles
  • First quartile (Q1) (lower quartile) (25th percentile)
  • Median (Q2) (50th percentile)
  • Third quartile (Q3) (75th percentile)
  • Order values in increasing order, split at median
    • Everything to the left is data for Q1, and to the right is Q3
IQR

The difference of Q1 and Q3

  • Resistant to outliers, usable to show center when data isn’t symmetrical

  • Identifying outliers

    • Value is an outlier if less than Q1-(1.5 x IQR) or greater than Q2-(1.5 x IQR)
Five Number Summary
  1. Minimum
  2. Lower Quartile (Q1)
  3. Median (Q2)
  4. Higher Quartile (Q3)
  5. Maximum
Additive Transformation
  • When a constant is added or subtracted from the original values
  • Shifts center by that amount (mean/median)
  • Doesn’t affect spread or shape (IQR, Range, SD)
Multiplicative Transformation
  • When a constant multiplies or divides all original values
  • Affects center (mean/median)
  • Affects spread (IQR, Range, SD)
  • Doesn’t affect spread