Advanced Statistics: Standard Deviation, Normal Distribution, and Data Sets
Advanced GRE Quantitative questions on statistics frequently test conceptual understanding of standard deviation rather than computational skill. Key concepts: standard deviation measures the average distance of data points from the mean. A data set with all identical values has a standard deviation of zero. Adding a constant to every value in a data set does not change the standard deviation (it shifts all values equally). Multiplying every value by a constant multiplies the standard deviation by the same constant (absolute value). The GRE tests these properties with Quantitative Comparison questions like: 'Set A = {2, 4, 6, 8, 10}; Set B = {12, 14, 16, 18, 20}. Compare the standard deviations.' Both sets have the same standard deviation because B is A shifted by 10 — standard deviation is unaffected by uniform shifts. Normal distribution concepts appear in data interpretation problems: in a normal distribution, approximately 68% of values fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three. Box plots (box-and-whisker plots) test knowledge of median, quartiles, and interquartile range (IQR = Q3 - Q1). The IQR measures the middle 50% of data and is a more robust spread measure than range for distributions with outliers. Scatter plots test understanding of correlation coefficients: a value near +1 indicates strong positive correlation, near -1 indicates strong negative correlation, near 0 indicates no linear correlation.