Description

📊 Z-Score Calculator – Measure Standard Deviations Easily

The Z-Score Calculator is a powerful statistical tool that helps students, teachers, researchers, and professionals understand how far a data point is from the mean of a dataset. Whether for hypothesis testing, grading systems, or analyzing distributions, this calculator makes Z-scores simple and easy to interpret.

📘 What It Calculates:

✅ Z-Score from Raw Score (e.g., given x, μ, σ → find z)

✅ Raw Score from Z-Score (e.g., given z, μ, σ → find x)

✅ Sample or Population Data – supports both types

✅ Step-by-Step Calculations for clarity

✅ Probability Insights using the standard normal distribution curve

💡 Features:

• Easy input for raw scores, mean, and standard deviation

• Automatic step-by-step solution with explanations

• Works with normal distribution for probability analysis

• Helps detect outliers, unusual values, or relative positions

• Great for academic learning and professional analysis

👤 Who Should Use This:

📌 Students & Teachers – for statistics, probability, and exam prep
📌 Researchers – to assess normality and detect outliers
📌 Psychologists & Social Scientists – to interpret standardized test scores
📌 Finance Analysts – to evaluate investment performance relative to benchmarks

🧮 Formula Used:

Z-Score Formula:

z=x−μσz = \frac{{x - \mu}}{{\sigma}}z=σx−μ​

Where:

• z = Z-score

• x = raw data value

• μ = mean

• σ = standard deviation

Inverse Formula (to find x):

x=z⋅σ+μx = z \cdot \sigma + \mux=z⋅σ+μ

📌 Example:

• Raw score: x = 85

• Mean: μ = 75

• Standard deviation: σ = 5

z=85−755=2z = \frac{{85 - 75}}{5} = 2z=585−75​=2

👉 Interpretation: The score is 2 standard deviations above the mean.

✅ Pro Tip:

Don’t just calculate—interpret the Z-score. Knowing whether a value is typical, unusual, or an outlier provides deeper statistical insight.

🔗 Related Tools You May Find Helpful:

➗ Standard Deviation Calculator – Find variability in data
📈 Root Calculator – Probability & curve analysis
🧮Ratio Calculator – Understand central tendency