Data Analytics: Foundations to Practice · Descriptive Statistics Fundamentals
Measures of Central Tendency
Mean, median, and mode all describe a dataset's 'typical' value, but they can diverge substantially, and picking the wrong one for a given dataset produces a genuinely misleading summary. This chapter covers when each is the right choice.
The mean, or average, sums all values in a dataset and divides by the count of values, giving a single number that incorporates every data point's exact value; this makes the mean sensitive to every value in the dataset, including extreme outliers, which can pull it substantially away from what most individual values actually look like.
Key Takeaways
- The mean incorporates every value's exact magnitude, making it sensitive to extreme outliers pulling it away from a dataset's typical value.
- The median depends only on position, making it far more resistant to outlier distortion, which is why it's often preferred for skewed data like income.
- The mode is the most frequently occurring value, the only central tendency measure available for purely categorical data.
- Choosing the right measure depends on distribution shape and data type; reporting a mean without checking distribution shape is a common, avoidable error.