Mean, median, standard deviation, combinatorics, and probability concepts tested on the GMAT quant section. Front: the term or formula. Back: definition or formula with a brief usage note.
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- Mean (arithmetic average)
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The sum of all values divided by the number of values. Used to find central tendency when data is roughly symmetric.- Median
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The middle value when data is ordered. The 50th percentile; preferred when data contains outliers.- Mode
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The value appearing most frequently in a dataset. May not exist or may not be unique.- Range
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The difference between the largest and smallest values. Simplest measure of spread.- Variance
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The average of squared deviations from the mean. Measured in squared units; standard deviation is its square root.- Standard deviation
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The square root of variance. Measures spread in original units; roughly 68% of data falls within one SD of the mean in a normal distribution.- What does small standard deviation indicate?
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Data points cluster closely around the mean; values are relatively consistent.- Z-score
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The number of standard deviations a value is from the mean. Formula: (value - mean) / standard deviation. Used to standardize scores.- Normal distribution
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A symmetric bell-shaped distribution where mean, median, and mode are equal. About 95% of data falls within two standard deviations of the mean.- Quartiles
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The three values (Q1, Q2, Q3) dividing ordered data into four equal groups of 25% each. Q2 is the median.- Interquartile range (IQR)
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The difference between Q3 and Q1. Contains the middle 50% of the data.- Probability (basic definition)
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A number between 0 and 1 representing likelihood of an event. P(event) = (favorable outcomes) / (total possible outcomes).- Sample space
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The set of all possible outcomes of an experiment or random process.- Mutually exclusive events
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Events that cannot occur simultaneously; P(A and B) = 0. Addition rule: P(A or B) = P(A) + P(B).- Independent events
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Events where one's occurrence does not affect the other's probability. Multiplication rule: P(A and B) = P(A) * P(B).
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