SAT statistics questions combine calculations with interpretation. You may compare mean and median, reason about spread and outliers, or decide whether a sample and study design justify a conclusion.
Essential concepts
Arithmetic mean
\[ar{x}= rac{x_1+x_2+cdots+x_n}{n}\]
The mean uses every value and is sensitive to outliers; the median depends on ordered position and is more resistant.
SAT strategy and application
Worked example
Compare mean and median with an outlier
For the data \(4,5,5,6,20\), compare the mean and median.
Find the median
The ordered middle value is 5.
Find the mean
\((4+5+5+6+20)/5=8\).
The mean is 8 and the median is 5; the high outlier pulls the mean upward.
Mistakes and traps
Mini check
Check your understanding
A random sample is selected from all students at a school. What does the random sampling primarily support?
A causal conclusion
Generalization to the school’s student population
Elimination of every source of bias
A larger standard deviation
Show answer and explanation
Answer: Generalization to the school’s student population
Random sampling makes the sample more representative of the population; it does not by itself create a randomized experiment.
Key takeaways
Key takeaways
What to remember
Interpret measures of center together with measures of spread.
Remember that the mean is more sensitive to outliers than the median.
Use random sampling for generalization and random assignment for causation.
Keep statistical conclusions within the scope of the data and design.
Continue learning
Put these notes into practice
Apply the ideas with SAT-style questions, then reinforce key details with flashcards.