Understanding Descriptive Statistics
Descriptive statistics summarize and describe the main features of a dataset. They provide simple measures that capture the central tendency, spread, and shape of data, forming the foundation of quantitative analysis in science, business, and everyday decision-making.
Measures of Central Tendency
The mean (arithmetic average) is the sum of all values divided by the count. The median is the middle value when data is sorted, making it resistant to outliers. The mode is the most frequently occurring value.
Mean = Σx / n | Variance = Σ(x - μ)² / n
Measures of Spread
The range is the difference between the maximum and minimum values. Variance measures how far values deviate from the mean on average (squared), and standard deviation is the square root of variance, expressed in the same units as the data.
When to Use Each Measure
Use the mean for symmetric distributions without extreme outliers. Choose the median for skewed data or when outliers are present. The mode is best for categorical data or identifying the most common value in a set.
Frequently Asked Questions
What is the difference between population and sample standard deviation?
Population standard deviation divides by N (total population size), while sample standard deviation divides by N-1 (Bessel's correction). This tool calculates the population standard deviation by default.
Can a dataset have more than one mode?
Yes. A dataset with two modes is called bimodal, and one with more than two is multimodal. If no value repeats, the dataset has no mode.