Mean, Median, Mode, and Standard Deviation

SAT Math · Axiom Academy

Mean, Median, Mode & Standard Deviation Master measures of central tendency and spread These statistics describe the "center" or typical value of a dataset. The SAT frequently asks which measure best describes a dataset, especially when outliers are present. Formula: Sum of all values ÷ Number of values Use when: Data is fairly evenly distributed Affected by: Outliers (extreme values) Definition: The middle value when data is ordered Use when: Data has outliers or skewed distribution Affected by: Order of data, not magnitude Definition: The value that appears most often Use when: You want the most common value Affected by: Only by frequency, not value size Calculating Mean, Median, and Mode Median: (5 + 7) ÷ 2 = 6 (average of middle two values) Mode: 5 (appears twice, all others appear once) Dataset: 2, 3, 4, 5, 50 (note: 50 is an outlier) Insight: The mean (12.8) is pulled high by the outlier, while the median (4) is more representative of the typical values. These measures show the spread or variability of data. Ordered dataset: 2, 4, 5, 7, 8, 9, 10, 12, 15 Standard deviation measures how spread out the data is from the mean. A larger standard deviation means data is more spread out; a smaller one means data is clustered near the mean. Example 4: Comparing Standard Deviations Dataset A: 4, 5, 5, 5, 6 (all values close to mean of 5) Dataset B: 1, 3, 5, 7, 9 (values spread across range) Dataset A has a smaller standard deviation (data is tightly clustered).

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