Summary of Quantitative Variables and Statistics Concepts

Dotplots

  • Created using an axis with an appropriate scale for dataset values.
  • Each dot represents a data point; multiple values stack vertically.

Common Shapes of Distributions

  • Symmetric: Both sides match when folded on center line.
  • Skewed Right: Piled up on left; tail extends right.
  • Skewed Left: Piled up on right; tail extends left.
  • Bell-shaped: Symmetric, with one mode.

Outliers

  • An outlier is significantly different from the rest of the dataset (much larger/smaller).

Mean

  • Calculated as: Mean = \frac{\text{Sum of all data values}}{\text{Number of data values}}
  • Denoted by \bar{x} (sample) or \mu (population).

Median

  • Middle value in ordered data:
    • Odd entries: middle entry.
    • Even entries: average of two middle values.

Resistance

  • A statistic is resistant if it's unaffected by extreme values.
  • Median is resistant; mean is not.

Example Calculations

  1. Ants on a Sandwich:
    • Original counts: 43, 59, 22, 25, 36, 47, 19.
    • New counts (with an extreme value): 43, 159, 22, 25, 36, 47, 19.
    • Compare means and medians before and after.