1. What Are Mean and Standard Deviation?

The mean is the average of all numbers in a dataset. The standard deviation measures how spread out the numbers are from the mean. Together they describe the central tendency and variability of data.

2. How Does the Calculator Work?

The calculator uses these formulas:

Where:

• \( x_i \) — Individual data points
• \( n \) — Number of data points
• \( \sum \) — Summation of all values

Explanation: The mean gives the central value, while standard deviation shows how much variation exists from the mean.

3. Importance of These Statistics

Details: These are fundamental statistics used in virtually all fields of research and data analysis to summarize and understand datasets.

4. Using the Calculator

Tips: Enter numbers separated by commas (e.g., 1, 2, 3, 4). At least two numbers are required to calculate standard deviation.

5. Frequently Asked Questions (FAQ)

Q1: When should I use population vs sample standard deviation?
A: Use sample standard deviation (n-1 denominator) when working with a sample of a larger population. Use population standard deviation (n denominator) when you have all data points.

Q2: What does a high standard deviation indicate?
A: A high standard deviation means data points are spread out over a wider range of values.

Q3: Can I calculate these for non-numerical data?
A: No, these calculations require numerical data that can be meaningfully averaged.

Q4: How many decimal places should I report?
A: Typically report one more decimal place than the original measurements.

Q5: What if my data contains outliers?
A: Consider using median and interquartile range instead, as mean and SD are sensitive to outliers.