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