Exploring One-Variable Data and Collecting Data

Thirteen topics on reading data before doing anything else to it. Variables and which displays fit them, histograms, dotplots and boxplots and what each one hides, shape, center, variability and outliers as a complete description, comparing distributions in actual comparative sentences, and where data comes from: random sampling, the bias no sample size can fix, and experimental design, where random assignment is what buys a causal claim.

Exam weight 20-30%13 topics

Topics

1.1

Introducing Statistics: What Can We Learn from Data?

Variables

Tabular Representation and Summary Statistics for One Categorical Variable

Graphical Representations for One Categorical Variable

Graphical Representations for One Quantitative Variable

Descriptions for One Quantitative Variable Distributions

Summary Statistics for One Quantitative Variable

Graphical Representations of Summary Statistics for One Quantitative Variable

Comparisons of the Distributions for One Quantitative Variable

The Investigative Question Revisited and Data Collection

Random Sampling

Potential Problems with Sampling

Experimental Design

Lesson

Diagnostic

after diagnostic

Key forms For every problem in this unit

Complete description

shape, center, variability, unusual features, IN CONTEXT with units

Skew direction

named for the TAIL: tail right → skewed right, even though the pile sits left

Mean x̄

sum of values / n. Follows the tail; one outlier can drag it

Median

middle of the ordered list. Resistant to outliers and skew

Standard deviation s

typical distance from the mean. Never negative; 0 only if all values equal

IQR

Q3 − Q1. A DISTANCE (spread), not a location

Outlier fences

below Q1 − 1.5·IQR or above Q3 + 1.5·IQR

Boxplot regions

each whisker-to-quartile stretch holds about 25% of the data, whatever its width

Skewed data summary

median + IQR (resistant pair); mean + SD for roughly symmetric data

Population vs sample

parameter describes the population; statistic describes the sample

Simple random sample

every group of size n has an equal chance. Haphazard is not random

Stratified

split into similar groups, sample WITHIN every group

Cluster

split into mini-populations, take ENTIRE randomly chosen groups

Bias

a property of the METHOD. A bigger sample repeats the mistake more times

Random selection

buys generalization to the population

Random assignment

buys cause-and-effect. The two are not interchangeable

Confounding

a third variable linked to BOTH the explanatory variable and the response

Experiment essentials

comparison, random assignment, control of other variables, replication

Unit 1 tools

Challenge bank

1 / 60

60 open-ended problems.

Read the question, work it out, then flip the card to compare your reasoning to the worked solution. Mark each card so you can return to the ones that still bite.

Question

Tap card to reveal explanation

Worked solution

Tap card to return to question

Cumulative assessment

Test the unit.

Twenty mixed items drawn from across all 13 topics, with guaranteed misconception-code coverage. Identifies which misconceptions still bite when you cannot see which topic the question came from.