14.2 Data distribution and outlier detection

Understanding data distribution and detecting outliers are crucial skills in exploratory data analysis. These techniques help you grasp the overall shape, spread, and central tendency of your data, revealing important patterns and potential anomalies.

By mastering visualization tools like histograms and boxplots, along with statistical measures like skewness and kurtosis, you'll be better equipped to interpret your data. Outlier detection methods further refine your analysis, ensuring you catch unusual observations that could impact your results.

Visualizing Data Distributions

Graphical Representations of Data

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• Histogram divides data into bins and displays frequency or count of observations in each bin
• Boxplot shows median, quartiles, and potential outliers in a compact form
• Density plot presents a smoothed representation of data distribution
• Q-Q plot compares sample quantiles to theoretical quantiles of a normal distribution

Interpreting Distribution Visualizations

• Histogram reveals overall shape, central tendency, and spread of data
• Boxplot identifies median, interquartile range, and potential outliers
• Density plot highlights peaks, valleys, and overall shape of distribution
• Q-Q plot assesses normality of data by comparing observed vs expected quantiles

Measures of Distribution Shape

Quantifying Distribution Characteristics

• Skewness measures asymmetry of distribution, indicating tail direction and magnitude
• Kurtosis quantifies heaviness of distribution tails compared to normal distribution
• Standard deviation calculates average distance of data points from mean
• Interquartile range (IQR) measures spread of middle 50% of data

Interpreting Shape Measures

• Positive skewness indicates right-skewed distribution with longer right tail
• Negative skewness suggests left-skewed distribution with longer left tail
• High kurtosis (leptokurtic) implies heavy tails and peaked distribution
• Low kurtosis (platykurtic) indicates light tails and flatter distribution

Outlier Detection Methods

Statistical Approaches to Outlier Identification

• Z-score measures number of standard deviations a data point is from mean
• Tukey's method uses IQR to define outliers as points beyond 1.5 * IQR from quartiles
• Cook's distance assesses influence of each observation on regression model
• Mahalanobis distance measures distance between point and distribution centroid in multivariate space

Applying Outlier Detection Techniques

• Z-score flags points exceeding threshold (typically 3 or -3) as potential outliers
• Tukey's method identifies outliers falling outside "whiskers" in boxplot
• Cook's distance highlights influential points in regression analysis
• Mahalanobis distance detects multivariate outliers considering covariance structure