Statistics for Data Science: From Basics to Inference

Statistics is the backbone of data science. It helps you turn raw numbers into clear answers, judge how sure you are about those answers, and decide what to do next. This guide walks through the basic ideas and shows how to use them in real projects.

Descriptive statistics

Descriptive statistics summarize data. Common tools are the mean, median, mode, range, and standard deviation. They describe what you see and can flag obvious problems, like a strange outlier or a skewed distribution. A quick example: a dataset with daily users over a month has an average of 3,200 visits per day and a standard deviation of 480. This tells you not just the size of the audience, but how stable it is.

From samples to decisions

In data work we rarely see the whole population. We collect samples and use them to infer about the larger group. The key idea is representativeness: the sample should reflect the population, so results are meaningful. Random sampling helps reduce bias, and careful data cleaning improves reliability.

Estimation and uncertainty

Estimation gives a single number (a point estimate) and also a sense of where the true value lies. Confidence intervals are a common tool: they say we are confident that the real value sits inside a range. For example, from a study of 2,000 users, a mean time on site of 2.8 minutes can have a 95% interval of roughly 2.76 to 2.84 minutes, assuming normal data. The exact width depends on sample size and variability.

Hypothesis testing and regression

Hypothesis testing asks if an observed effect is likely real or a fluke. P-values inform this, but they do not prove truth. Regression models estimate relationships between variables and help predict outcomes. Coefficients describe how much a unit change in one variable moves the result, within the chosen model’s assumptions. Always check these assumptions before trusting conclusions.

A practical workflow

  • Explore data quickly to spot trends.
  • State a simple question and choose an appropriate method.
  • Check assumptions, then estimate and report uncertainty.
  • Communicate results clearly with visuals and honest caveats.

This approach keeps analyses honest and useful for decision makers. Beyond basic methods, Bayesian statistics offer a different view of uncertainty. Instead of a fixed interval, you update beliefs as new data arrives. This flexibility is handy in data science tasks like online experiments or forecasting.

Key Takeaways

  • Descriptive statistics summarize data and reveal patterns.
  • Estimation and confidence intervals quantify uncertainty in results.
  • Clear reporting, checking assumptions, and using appropriate methods improve credibility.