1. What is Standard Deviation?

Standard Deviation (SD) is a measure of how spread out numbers are from their mean value. It quantifies the amount of variation or dispersion in a set of data values.

2. How Does the Calculator Work?

The calculator uses the standard deviation formula:

Where:

• \( SD \) — Standard deviation
• \( x_i \) — Each individual value in the dataset
• \( \text{mean} \) — Arithmetic mean of all values
• \( n \) — Number of values in the dataset

Explanation: The formula calculates the square root of the average of the squared differences from the mean (for a sample, using n-1 denominator).

3. Importance of Standard Deviation

Details: Standard deviation is crucial in statistics for understanding data variability. A low SD indicates data points are close to the mean, while high SD indicates data are spread out over a wider range.

4. Using the Calculator

Tips: Enter comma-separated numerical values (e.g., "5, 10, 15"). The calculator will compute standard deviation, mean, and count of values. At least two values are required.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between population and sample SD?
A: Population SD divides by n, sample SD divides by n-1 (Bessel's correction). This calculator uses sample SD.

Q2: When should I use standard deviation?
A: Use SD when you need to quantify dispersion in normally distributed data. For skewed distributions, consider interquartile range.

Q3: What does a standard deviation of 0 mean?
A: SD=0 indicates all values in the dataset are identical (no variation).

Q4: How is standard deviation related to variance?
A: Variance is the square of standard deviation. SD has the same units as the original data.

Q5: What's a "good" standard deviation?
A: There's no universal "good" value - interpretation depends on context and the data's mean value.