Home / Courses / SAT Math / Unit 6

SAT Math Unit 6: Data, statistics & probability

Data questions ask you to read tables and graphs, compare centers and spreads, and reason about samples and probability.

Covers: Mean, median and spread, two-way tables, conditional probability, scatterplots, margin of error and sampling

Study guide

The mean is the average; the median is the middle value of sorted data. Outliers pull the mean toward them but barely move the median, so a skewed data set has its mean pulled toward the tail. Range and standard deviation measure spread: a larger standard deviation means values are more spread out around the mean. Adding the same number to every value shifts the center but not the spread.

Two-way tables organize counts by two categories. To find a probability, divide the count you want by the total of the group you're choosing from. Conditional probability, P(A given B), restricts you to the B row or column: use the B total as the denominator.

Scatterplots show relationships between two quantitative variables. A line of best fit summarizes the trend; its slope is the predicted change in y per unit of x, and you can use it to estimate values. Predicting far outside the data's range is risky.

Sampling questions test what conclusions are allowed. A random sample from a population lets you generalize to that population, and a margin of error gives a range where the true value plausibly lies. Larger samples give smaller margins of error. Only a randomized experiment, not an observational study, supports cause-and-effect conclusions.

When data are given as values with frequencies, the mean is Σ(value × frequency) ÷ Σ(frequency). The median is the middle position in the total count, found by adding frequencies until you reach that position. On a dot plot or histogram, the data set with more values far from the center has the larger standard deviation. A data set that is bunched tightly around its mean has a smaller one, even if its range is similar.

To estimate the slope of a line of best fit, pick two points on the line (not necessarily data points) that are far apart and easy to read, then compute rise over run.

Key ideas

• Mean is pulled by outliers; median is resistant.
• Standard deviation measures typical distance from the mean.
• Conditional probability: restrict to the given row or column of a two-way table.
• A margin of error gives a range of plausible values for the population.
• Conclusions only generalize to the population that was randomly sampled.

Formulas and rules

Common mistakes

• Using the grand total as the denominator for a conditional probability.
• Treating a sample estimate as the exact population value.

Words to know

Outlier sensitivity

The mean is pulled by outliers; the median resists them.

P(A | B) from a two-way table

(A and B count) ÷ (B total).

Margin of error

± range around an estimate where the true value plausibly lies.

Standard deviation

A measure of how spread out values are around the mean.

Random sample

Selected by chance from a population, so results can generalize to it.

Mean

The average: sum ÷ count.

Median

The middle value of sorted data.

Range

Maximum minus minimum.

Two-way table

A table of counts for two categorical variables.

Conditional probability

P(A given B): use the B group's total as the denominator.

Line of best fit

A line summarizing a scatterplot's trend, used to predict.

Observational study vs. experiment

Only randomized experiments support cause-and-effect conclusions.

Sample practice questions

271 more questions like these, from level 1 to 5, are in the practice set.