Statistics

SAT Math — Statistics and Data Analysis ## Measures of Center Mean (Average): Sum of all values ÷ number of values > {3, 7, 9, 11, 15} → Mean = (3 + 7 + 9 + 11 + 15)/5 = 45/5 = 9 Median: The middle value when data is ordered. If there's an even number of values, average the two middle ones. > {3, 7, 9, 11, 15} → Median = 9 (middle value) > {3, 7, 9, 11} → Median = (7 + 9)/2 = 8 Mode: The most frequently occurring value. When to use which: - Mean is affected by outliers (extreme values) - Median is better for skewed distributions or when outliers are present - Use median for home prices, income distributions, etc. ## Spread: Range and Standard Deviation Range: Maximum − Minimum > {3, 7, 9, 11, 15} → Range = 15 − 3 = 12 Standard deviation: Measures how spread out values are from the mean. The SAT tests conceptual understanding, not calculation. - Small standard deviation: Data is clustered close to the mean - Large standard deviation: Data is spread far from the mean ## Sampling and Inference The SAT tests your ability to evaluate the validity of statistical conclusions. Representative sample: A sample that reflects the population's characteristics. Random sampling produces representative samples. Margin of error: The uncertainty range around a sample estimate. A survey result of "60% ± 3%" means the true value is likely between 57% and 63%. Bias: When a sample systematically misrepresents the population. - Voluntary response bias: People with strong opinions are more likely to respond - Convenience sampling: Only surveying people who are easy to…