Summarising data

data distribution: we want to know what the data looks like

a good summary needs to show location, spread, range, extremes, gaps/holes, symmetry, etc.

Graphical summaries

Frequency distribution (table)

Bar chart

Pareto bar chart

orders categories based on frequency. only for nominal level of measurement

Pie chart

size of pieces of pie shows frequency of category.

Histogram

size of bar shows frequency of that category.

Time series

shows quantity that varies over time.

Descriptive summaries

qualitative description:

• shape:

  

• location: position on x axis (around 0, around 10, etc.)

• dispersion: spread out graph == large dispersion

numerical description:

• location: measure of center
  • mean: average (sum everything, divide by the total number)
  • median: sort, find the middle number
  • mode: most often occurring value (highest frequency)
    • unimodal: unique mode
    • bimodal: two modes
    • multimodal: more than two modes
• dispersion:
  • measures of variation
    • sample standard deviation (how much values deviate from mean)
      • same units as data (unlike variance)
      • standard deviation is $\sqrt{s^{2}}$
      • $s^{2} = \frac{\sum_{i=1} n(x_{i} - \bar{x}^{2})}{n-1}$
      • for population: σ², σ
    • range
      • (minimum - maximum)
      • sensitive to extreme values
  • relative standing
    • percentiles, quartiles (special percentiles: Q1, Q2 (median), Q3)
    • IQR: interquartile range = (Q3 - Q1)
    • 5-number summary: min, Q1, median (Q2), Q3, max
      • boxplot is graph of this
      • whiskers are lines from box (by default, not more than 1.5 × IQR
      • outliers: points outside of whiskers