1. What is Mean and Standard Deviation?

The mean is the average of all data points, while standard deviation (SD) measures how spread out the numbers are from the mean. Together they provide a basic statistical description of a dataset.

2. How Does the Calculator Work?

The calculator uses these formulas:

Where:

• \( x \) — Individual data points
• \( n \) — Number of data points
• \( \sum \) — Sum of all values
• \( \text{mean} \) — Average of the data

Explanation: The mean gives the central tendency while SD quantifies the amount of variation in the dataset.

3. Importance of Mean and SD

Details: These are fundamental statistics used in virtually all fields of research. The mean shows where values cluster, while SD indicates how much they vary.

4. Using the Calculator

Tips: Enter numeric values separated by commas. The calculator will ignore any non-numeric entries. At least 2 data points are needed for SD calculation.

5. Frequently Asked Questions (FAQ)

Q1: When should I use mean vs median?
A: Use mean for normally distributed data without outliers. Use median for skewed distributions or when outliers are present.

Q2: What does a high standard deviation mean?
A: A high SD indicates that data points are spread out over a wider range of values from the mean.

Q3: Can SD be negative?
A: No, standard deviation is always a non-negative value since it's derived from squared differences.

Q4: Why n-1 in the SD denominator?
A: Using n-1 (Bessel's correction) gives an unbiased estimate of the population SD when working with a sample.

Q5: How many decimal places should I report?
A: Typically report one more decimal place than the original measurements, but context matters.