AWS Certified Machine Learning – SpecialtyExploratory Data AnalysisMedium
A data scientist is analyzing a dataset containing customer ratings for various products on an e-commerce platform. The ratings are on a scale of 1 to 5. They want to understand the central tendency and spread of these ratings. However, they observe that the distribution of ratings is heavily concentrated at 5 stars, with a long tail of lower ratings (left-skewed). They need a robust measure of central tendency and spread that is not unduly influenced by this skewness. Which pair of statistical measures would be most appropriate?
- AMedian and Interquartile Range (IQR).
- BGeometric Mean and Variance.
- CMean and Standard Deviation.
- DMode and Range.
Show answer & explanationAnswer & explanation
Correct answer: A. Median and Interquartile Range (IQR).
For skewed distributions, the median is a more robust measure of central tendency than the mean, as it is less affected by extreme values. Similarly, the Interquartile Range (IQR) is a robust measure of spread, as it describes the spread of the middle 50% of the data, making it less sensitive to the long tail of a skewed distribution compared to the standard deviation.
Why the other options are wrong
- B. Incorrect. Geometric mean is used for data that grows exponentially or for ratios, not typically for skewed ordinal ratings. Variance is also sensitive to skewness and outliers, similar to standard deviation.
- C. Incorrect. Mean and standard deviation are highly sensitive to skewness and outliers, which would misrepresent the central tendency and spread in a heavily skewed distribution.
- D. Incorrect. While the mode might capture the most frequent rating (5 stars), the range is highly sensitive to extreme values, and neither fully captures the overall central tendency and robust spread as effectively as median and IQR for skewed data.
Robust Statistics for Skewed Data
Statistical measures of central tendency and spread that are less affected by extreme values or deviations from normality, making them suitable for skewed distributions.
- Median is a robust measure of central tendency.
- Interquartile Range (IQR) is a robust measure of spread.
- These measures are preferred over mean and standard deviation for skewed data.
Memory trick: Skewed data's tale: Median and IQR prevail.