Describing quantitative distributions and summary statistics

Learning objectives

Construct and interpret dotplots, stem-and-leaf plots and histograms for a quantitative variable, and explain how the choice of interval width changes the appearance of a histogram

Describe a distribution in context by its shape, center, variability and unusual features, using the terms skewed right, skewed left, symmetric, unimodal, bimodal, uniform, outlier, gap and cluster

Calculate and interpret the mean, median, quartiles, percentiles, range, interquartile range and sample standard deviation, and justify using the resistant measures, the median and IQR, for a skewed distribution or one with outliers

Identify outliers with the 1.5 × IQR rule and with the rule of two standard deviations from the mean, construct a boxplot from the five-number summary, and relate the positions of the mean and the median to the direction of skew

Compare two or more distributions of the same variable using back-to-back stem-and-leaf plots, dotplots, histograms or boxplots on a common scale, making explicit comparative statements about shape, center, variability and outliers

Predict how a change of units alters each summary statistic, calculate a z-score as the number of standard deviations a value lies from the mean, and use z-scores to compare the relative position of values from different distributions