Guided route
Follow the selected readings and build the final output.
This introductory route covers selected foundations, not the entire field.
Finding the next step…
piatra . institutepathwayspiatra . institutepathwaysFinding the next step…
Describe data, examine a sample and write a report with clear limits.
Arithmetic with fractions and percentages. Use a calculator or spreadsheet; calculus and programming are not required. The Probability route helps with optional inference readings.
A small data report with a chart, reproducible summaries and a defensible conclusion.
Start here if the background is new. Equivalent experience is enough.
Use probability for the optional confidence-interval and hypothesis-test readings; the first data report needs only arithmetic.
Barbara Illowsky · Susan Dean · reference
1.1 Definitions of Statistics, Probability, and Key Terms
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Open the readingBarbara Illowsky · Susan Dean · reference · 2023
1.3 Frequency, Frequency Tables, and Levels of Measurement
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Open the readingStatistics: terminology. Define the population, sample, observational unit and variable in one question.
Introductory Statistics 2e: 1.3 Frequency, Frequency Tables, and Levels of Measurement. Classify your variables and make a frequency table.
Barbara Illowsky · Susan Dean · reference
2.5 Measures of the Center of the Data
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Open the readingBarbara Illowsky · Susan Dean · reference · 2023
2.6 Skewness and the Mean, Median, and Mode
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Open the readingBarbara Illowsky · Susan Dean · reference
2.7 Measures of the Spread of the Data
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Open the readingBarbara Illowsky · Susan Dean · reference
2.2 Histograms, Frequency Polygons, and Time Series Graphs
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Open the readingStatistics: centre. Calculate mean and median and explain what each summarises.
Introductory Statistics 2e: 2.6 Skewness and the Mean, Median, and Mode. Compare a centre with and without one unusually large observation.
Statistics: spread. Describe spread and keep the units visible.
Statistics: histograms. Compare two bin choices and label axes and units.
For this invented set of reading-session lengths in minutes — 3, 4, 4, 5, 24 — calculate the mean, median and range. Why might “the average session is 8 minutes” be incomplete?
Sort the observations, keep the units and notice the unusually long session.
The sum is 40 minutes, so the mean is 40/5 = 8 minutes. The middle observation is 4, so the median is 4 minutes. The range is 24 − 3 = 21 minutes. One long session raises the mean; reporting the median, spread, five observations and the display gives a fuller account. Neither summary by itself describes all learners or explains why the long session occurred.
What to look for
Common mistake: Reporting a precise mean as though it described a representative population.
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Barbara Illowsky · Susan Dean · reference
1.2 Data, Sampling, and Variation in Data and Sampling
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Open the readingBarbara Illowsky · Susan Dean · reference
1.4 Experimental Design and Ethics
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Open the readingStatistics: data and sampling. Compare sampling methods and explain who a convenience sample leaves out.
Statistics: experimental design. Distinguish random sampling from random assignment and consider consent.
In an invented app poll, 12 of 15 volunteers say they study every day. Can you report that 80% of all students study every day? What is a defensible report?
Calculate the sample proportion, then examine recruitment and the target population.
12/15 = 0.8, so 80% of these 15 app volunteers reported studying every day. This self-selected group may differ from other students, and the question measures a report rather than verified behaviour. A claim about all students would need a defined target population and a defensible sampling and measurement plan. Increasing the number of volunteers alone would not remove selection bias.
What to look for
Common mistake: Assuming that a large convenience sample automatically removes systematic bias.
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Barbara Illowsky · Susan Dean · reference · 2023
12.2 Scatter Plots
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Open the readingBarbara Illowsky · Susan Dean · reference
1.4 Experimental Design and Ethics
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Open the readingIntroductory Statistics 2e: 12.2 Scatter Plots. Draw a scatter plot and separate association from a causal explanation.
Statistics: experimental design. Distinguish random sampling from random assignment and consider consent.
Barbara Illowsky · Susan Dean · reference
1.2 Data, Sampling, and Variation in Data and Sampling
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Open the readingBarbara Illowsky · Susan Dean · reference · 2023
2.4 Box Plots
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Open the readingBarbara Illowsky · Susan Dean · reference · 2023
12.2 Scatter Plots
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Open the readingStatistics: data and sampling. Compare sampling methods and explain who a convenience sample leaves out.
Introductory Statistics 2e: 2.4 Box Plots. Use a box plot to compare centres and spreads without hiding the sample size.
Introductory Statistics 2e: 12.2 Scatter Plots. Draw a scatter plot and separate association from a causal explanation.
An invented report finds that people who practise more also score higher. Its conclusion says, “Adding one hour of practice will raise anyone’s score.” Explain the gap and write a more careful conclusion.
An observed difference between people is not automatically the effect of changing one person’s behaviour.
The report describes an association in the observed group. Prior knowledge, motivation, access to help or other differences could influence both practice and score. A careful conclusion is that more practice was associated with higher scores in this sample; the report does not establish the effect of adding an hour for any particular person. A justified causal design and appropriate measurements would be needed for a stronger claim.
What to look for
Common mistake: Turning a correlation into a guaranteed effect for every individual.
Start this pathway to keep your answers in My learning.
Editorial perspectives based on selected works, rather than author-endorsed reading lists.
Follow the selected readings and build the final output.
This introductory route covers selected foundations, not the entire field.
Focus on faithful summaries of the observations.
A careful display cannot make an unrepresentative sample representative.
Focus on recruitment, measurement and the reach of the conclusion.
Inference formulas do not repair a flawed collection design.
Background, different viewpoints, and further reading.
Define the population, sample, observational unit and variable in one question.
1.1 Definitions of Statistics, Probability, and Key Terms
Compare sampling methods and explain who a convenience sample leaves out.
1.2 Data, Sampling, and Variation in Data and Sampling
Classify your variables and make a frequency table.
1.3 Frequency, Frequency Tables, and Levels of Measurement
Distinguish random sampling from random assignment and consider consent.
1.4 Experimental Design and Ethics
Choose a bar graph or a simple dot plot that fits your variable.
2.1 Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs
Compare two bin choices and label axes and units.
2.2 Histograms, Frequency Polygons, and Time Series Graphs
Locate quartiles; explain what a percentile says about the ordered data.
2.3 Measures of the Location of the Data
Use a box plot to compare centres and spreads without hiding the sample size.
2.4 Box Plots
Calculate mean and median and explain what each summarises.
2.5 Measures of the Center of the Data
Compare a centre with and without one unusually large observation.
2.6 Skewness and the Mean, Median, and Mode
Describe spread and keep the units visible.
2.7 Measures of the Spread of the Data
Review probability vocabulary before discussing uncertainty.
3.1 Terminology
Use the normal model as an assumption to assess, not a property of every dataset.
6.1 The Standard Normal Distribution
Distinguish a distribution of observations from a distribution of sample means.
7.1 The Central Limit Theorem for Sample Means (Averages)
Read the known-population-standard-deviation assumptions before using this interval.
8.1 A Single Population Mean using the Normal Distribution
Read the small-sample and t-interval assumptions for an unknown population spread.
8.2 A Single Population Mean using the Student t Distribution
Read the conditions for estimating a population proportion.
8.3 A Population Proportion
State null and alternative hypotheses before interpreting a test.
9.1 Null and Alternative Hypotheses
Describe false positive and false negative decisions in context.
9.2 Outcomes and the Type I and Type II Errors
Draw a scatter plot and separate association from a causal explanation.
12.2 Scatter Plots
Distinguish a measured task result from a population claim when comparing experiments.
Check samples and the limits of a comparison before interpreting growth data.
Practise a summary on new data and compare the result with a worked answer.