The Z-Score Calculator is a statistical tool designed to standardize data points and measure how far a value deviates from the mean in terms of standard deviations. It helps researchers, students, and analysts compare different datasets, detect outliers, and perform probability calculations.

Key Features

✅ Instant Z-Score Calculation – Computes Z-score using input values for mean and standard deviation.
✅ Supports Population & Sample Data – Choose between population-based or sample-based Z-scores.
✅ Probability Estimation – Determines the probability of a value occurring within a normal distribution.
✅ Graphical Representation – Displays standard normal distribution curves with highlighted Z-scores.
✅ PDF Report Generation – Export calculated results, probability insights, and distribution charts.

Use Cases

📌 Academic & Statistical Research – Standardize test scores and compare different datasets.
📌 Finance & Investment Analysis – Measure risk and volatility in stock prices.
📌 Quality Control & Manufacturing – Identify deviations in production quality.
📌 Healthcare & Psychology – Standardize medical test results and behavioral data.

How It Works

1️⃣ Enter Data – Input the raw value, mean, and standard deviation.
2️⃣ Run Calculation – The tool computes the Z-score using the formula:

$$Z = \frac{(X – \mu)}{\sigma}$$

where $X$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation.
3️⃣ Interpret Results – See how far the value is from the mean and its corresponding probability.
4️⃣ Visualize Distribution – View the normal distribution curve with the Z-score placement.
5️⃣ Download PDF Report – Export a summary with calculations and graphical insights.

This tool makes statistical analysis easier by quickly calculating and visualizing Z-scores for any dataset. 🚀