Statistics with Interactive Applets

Statistics is the discipline of collecting, summarising and drawing conclusions from data, and it divides broadly into descriptive and inferential parts. Descriptive statistics condense a data set into summary measures such as the mean, median and mode for central tendency, and the range, variance and standard deviation for spread. Graphical summaries including histograms, box plots and scatter diagrams reveal the shape of a distribution and the presence of outliers. Interactive applets allow these summaries to update in real time as data points are added or moved.

Probability provides the theoretical foundation for inference. The normal (Gaussian) distribution, with its symmetric bell shape, describes many natural measurements and underlies the central limit theorem, which explains why averages of samples tend toward a normal shape regardless of the original distribution. Applets that draw repeated random samples and accumulate their means make this convergence visible, helping to clarify ideas such as sampling variability and the standard error.

Inferential methods use samples to estimate properties of a larger population and to test hypotheses. Confidence intervals express the uncertainty in an estimate, while significance tests assess whether an observed effect is likely to be due to chance. Correlation and regression quantify and model relationships between variables, with a fitted line summarising how one quantity changes with another. Manipulating points on a scatter plot and watching the regression line and correlation coefficient respond builds an intuition for how these measures behave.

Frequently asked questions

What is the difference between descriptive and inferential statistics?

Descriptive statistics summarise the data at hand, while inferential statistics use a sample to draw conclusions about a wider population.

Why is the normal distribution so important?

Many measurements approximate it, and the central limit theorem shows that sample means tend toward a normal shape, which justifies many statistical tests.

What does a correlation coefficient measure?

It measures the strength and direction of a linear relationship between two variables, ranging from −1 for a perfect inverse relationship to +1 for a perfect direct one.