Which is better: mean or median?

It depends on the data. For symmetric distributions, they are similar. For skewed data or data with outliers, the median is more representative because it is not pulled by extreme values.

What does standard deviation tell me?

It tells you how spread out the data is. A standard deviation of 2 means most values are within 2 units of the mean. It quantifies variability.

Statistics

Data, averages, and distributions

Statistics is the science of data — collecting, analyzing, and interpreting information. The measures of central tendency (mean, median, mode) and spread (range, standard deviation, variance) are the foundation of statistical literacy.

Key Concepts

Mean

The average: sum of all values divided by the count. The most common measure of central tendency, but sensitive to outliers.

Median

The middle value when data is sorted. Not affected by outliers, making it better for skewed data like income.

Mode

The most frequently occurring value. Useful for categorical data. A dataset can have one mode, multiple modes, or no mode.

Standard Deviation

Measures how spread out the data is from the mean. Low SD = data clustered near the mean. High SD = data spread out.

Range

The simplest measure of spread: maximum minus minimum. Easy to calculate but sensitive to outliers.

Tips & Tricks

Use median instead of mean when data has extreme outliers (e.g. house prices, salaries).
Standard deviation = √variance. Always in the same units as the original data.
In a normal distribution, ~68% of data falls within 1 standard deviation of the mean.
The interquartile range (IQR) is more robust than range — it ignores the top and bottom 25%.