L1 part 1

• DATA, POPULATION, & SAMPLE

  • Data: Characteristics or information, usually numerical, collected through observation
  • Population: Collection of all items of interest to a study
  • Sample: Subset of the population
• DESCRIPTIVE STATISTICS

  • Alternative descriptive statistics
  • Advantages and disadvantages of alternative descriptive statistics
  • Comparing and contrasting different data using descriptive statistics
  • Advantages and disadvantages of alternative methods of displaying data
• CORRELATION VS. CAUSATION


  • Recognizing the difference between correlation and causation
  • Employing correlation to evaluate the relationship between two variables
• DATA – What exactly is it?
• Etymology of Data: Latin (verb “dare”), plural of Datum, something given or admitted especially as a basis for reasoning or inference
• Definition of Data: Characteristics or information, usually numerical, that are collected through observation
• Context of Data: Data is the physical representation of information in a manner suitable for communication, interpretation, or processing by human beings or by automatic means
• DATA – What types are there?
• Data Types

  • Quantitative (Numerical)
  • Qualitative (Categorical)
  • Discrete
  • Continuous
  • Nominal
  • Ordinal
• Examples of Data

  • Covid-19 cases and fatalities per day
  • Total flights per day worldwide
  • Total vehicle-miles travelled in major roadways
  • Number of rainy and sunny days per country
  • Traffic crashes around the Netherlands
• Population vs. Sample

  • Population: Collection of all items of interest to a study
  • Sample: Subset of the population
• Population (N): A population is the collection of all items of interest to a study. It does not only refer to people or animate creatures but also objects, events, procedures, or observations
• Sample (n): A sample is a subset of the population. An investigation is often restricted to one or more samples drawn from the population
• Data Analysis methods

  • Descriptive Statistics
  • Statistical Inference I
• Descriptive Statistics: methods and techniques for summarizing and interpreting data
• Descriptive Statistics are used to get to know a “population” by estimating a single value
• Descriptive Statistics components

  • Mean
  • Median
  • Mode
  • Skewness & Kurtosis
• Observations can be ordered from smallest to largest magnitude. The boundaries of the data to be defined and supports comparisons of the relative position of specific observations
• A percentile is defined as that value below which lies P% of the values in the remaining sample
• Percentile calculation formula: %iles = (R / n) * 100 where n=16
• What are the 25th, 50th, and 75th percentiles?


  1/4, 1/2, 3/4
• Percentiles

  Measures of the relative positions of points
• Median constitutes a measure of the centrality of the observations, or central tendency
• Central Tendency measures

  • Mean
  • Median
  • Mode
• Percentiles are useful for understanding the relative standing of data points
• Descriptive Statistics

  • Central Tendency – Mean, Median, Mode
• Percentiles

  Measures of the relative positions of points, with the middle percentile or "median" representing the centrality of the observations or central tendency
• Arithmetic mean


  The most popular and useful measure of central tendency, also known as the sample mean or expectation
• Sample mean or expectation of X

  x1, x2, ..., xn
• Population mean

  μ = 1/N * Σ(xi)
• The value that occurs most frequently, or the most commonly occurring outcome. Only applicable to Count data
• Advantages and Disadvantages of mean, median, and mode
• When data are symmetric and unimodal, the mode, median, and mean are approximately equal
• If the data are qualitative: mean or median, but mode
• Variability – Variance, Standard Deviation: Used to describe and quantify the spread or dispersion around the centre (e.g., mean)
• If the data are qualitative → mean:
• Used to describe and quantify the spread or dispersion around the centre (e.g., mean)
• average or expected value of a sample is not sufficient to understand data
• Can we measure variability by the difference between minimum and maximum observation?
• Or, what about difference between 25th and 75th percentiles?