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
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