Statistics Fundamentals

Statisticsbeginner~10 min

Compute descriptive statistics, fit distributions, run hypothesis tests, and cluster data.

Step 1 — Descriptive statistics

Summarize data with mean, standard deviation, and percentiles.

data = randn(1, 1000);
disp(mean(data));
disp(std(data));
disp(prctile(data, [25 50 75]))

Expected output: Mean near 0, std near 1, quartiles

Visualize data distribution.

data = randn(1, 500);
histogram(data);
title('Normal Distribution Sample')

Expected output: Bell-shaped histogram

ttest() returns an object with t-statistic, p-value, degrees of freedom, and confidence interval.

sample = 5 + 0.5*randn(1, 30);
result = ttest(sample, 5);
printf('p-value: %.4f, t-stat: %.2f', result.p, result.t)

Expected output: p-value and t-statistic

Group 2D data into clusters.

X = [randn(50,2); 3+randn(50,2)];
[idx, C] = kmeans(X, 2);
scatter(X(:,1), X(:,2));
title('K-means Clustering')

Expected output: Scatter plot with 2 visible clusters