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Principles of Statistics for Data Analysis

1Making sense of a pile of numbers

  • 1.1A pile of numbers has a middle
  • 1.2The average, and when it lies to you
  • 1.3The middle one: the median
  • 1.4What kind of data is this?
  • 1.5Before you summarise: missing and impossible values
  • 1.6The most common: the mode
  • 1.7The weighted average, and the mean from a frequency table
  • 1.8Other averages: the trimmed mean and the geometric mean
  • 1.9Which centre tells the truth?
  • 1.99Check yourself: making sense of a pile of numbers

2How spread out is it?

  • 2.1Same average, different story: the range
  • 2.2The middle half: quartiles and the IQR
  • 2.3Where do I stand? Percentiles and cumulative frequency
  • 2.4How far from the average? Variance in plain words
  • 2.5Standard deviation: the typical distance
  • 2.6A sample or the whole group? STDEV.S and STDEV.P
  • 2.7Comparing spread fairly: the coefficient of variation
  • 2.8Is this value unusual? Fences for outliers
  • 2.99Check yourself: how spread out is it

3The shape of data, and the right picture

  • 3.1Data has a shape: the dot plot and the stem-and-leaf plot
  • 3.2Histograms: sorting values into bins
  • 3.3Same data, different bins
  • 3.4Lopsided data: skew
  • 3.5The box plot: five numbers in one picture
  • 3.6Comparing groups side by side
  • 3.7Pictures for categories
  • 3.8Change over time: line charts, percentage change and percentage points
  • 3.9Two numbers for each thing: a first look at scatter plots
  • 3.99Check yourself: the shape of data

4Probability in plain language

  • 4.1What \"chance\" means
  • 4.2Chances from a table
  • 4.3Not, or, and
  • 4.4When one thing changes the chance: conditional probability
  • 4.5Chances in a row: the multiplication rule and tree diagrams
  • 4.6Independent or connected?
  • 4.7The base-rate surprise
  • 4.8Probability distributions and expected value
  • 4.99Check yourself: probability in plain language

5Counting chances: the binomial and the Poisson

  • 5.1Counting successes: when the binomial fits
  • 5.2Exact chances with BINOM.DIST
  • 5.3What to expect from a count: mean and spread
  • 5.4Waiting for the first success: the geometric distribution
  • 5.5Counts per day: the Poisson distribution
  • 5.6Many tries make a bell
  • 5.99Check yourself: counting chances

6The normal curve: where it fits and where it does not

  • 6.1From histogram to curve
  • 6.2The normal curve and its two dials
  • 6.3Most values sit close: the empirical rule
  • 6.4z-scores: how many steps from the middle?
  • 6.5Finding chances with NORM.DIST and NORM.INV
  • 6.6Is it normal? The Q-Q plot
  • 6.7When the bell does not fit
  • 6.8Taming skew with logs
  • 6.99Check yourself: the normal curve

7Samples, bias and study design

  • 7.1The whole pot and the spoonful: population and sample
  • 7.2Fair spoons: random sampling
  • 7.3Other fair spoons: stratified, cluster, systematic and multistage samples
  • 7.4How bias sneaks in
  • 7.5Watching or testing? Observational studies and experiments
  • 7.6Making an experiment fair: control, random assignment, replication, blocking, placebo and blinding
  • 7.7Collecting data ethically: consent, privacy and anonymising
  • 7.8Capstone: the Harbourside water and health survey
  • 7.99Check yourself: samples, bias and study design
  • 7.100Final exam: Principles of Statistics
Principles of Statistics for Data Analysis

Making sense of a pile of numbers

Check yourself: making sense of a pile of numbers

A quick self-check on types of data and the mean, median and mode.

Check yourself: making sense of a pile of numbers

What is next

A centre is only half the story. Module 2 measures how spread out the data is, which changes what the average really means.

PreviousWhich centre tells the truth? NextSame average, different story: the range
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