Data, Statistics, and Probability

Five topics on data and chance, the second half of the SAT's Problem-Solving and Data Analysis domain. Tables and graphs, center and spread, scatterplots and fit lines, probability, and sampling and claims. The errors here are reading errors: the wrong cell, the wrong denominator, the wrong measure, the claim a study never earned.

Topics

4.1

Tables and Graphs

Center and Spread

Scatterplots and Fit Lines

Probability

Sampling and Claims

Lesson

Diagnostic

after diagnostic

Reference The center, spread, probability, and study-design facts behind every problem in this unit

Mean (total over count)

$\bar{x} = \dfrac{\sum x}{n}$, so $\sum x = n\bar{x}$

Median (middle value of the ORDERED list)

even $n$: average the two middle values

Mode and range

mode = most frequent value; range = max $-$ min

Spread (standard deviation, compare by eye)

tighter cluster $\Rightarrow$ smaller SD; outliers pull the mean, not the median

Frequency table mean

$\bar{x} = \dfrac{\sum (\text{value} \cdot \text{frequency})}{\sum \text{frequency}}$

Probability (favorable over possible)

$P(A) = \dfrac{\#\ \text{favorable}}{\#\ \text{possible}},\quad 0 \le P \le 1$

Two-way table (condition on the ROW or COLUMN named)

$P(A \mid B) = \dfrac{\#\ \text{in both}}{\#\ \text{in } B}$

Line of best fit (slope = predicted change per unit of $x$)

$\hat{y} = mx + b$; a point above the line has positive residual

Sampling and claims

random sample $\Rightarrow$ generalize to the population; random assignment $\Rightarrow$ cause and effect

Margin of error

a larger sample gives a smaller margin; the estimate is a range, not a guarantee

Unit 4 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.

Mixed items pulled from across the unit's topics, with no labels showing which is which. It surfaces the misconceptions that still bite when you cannot tell what a question is testing.