1. What is Standard Deviation of Sample Mean?

The standard deviation of sample mean measures the dispersion of data points from their mean value when data is grouped into classes with frequencies. It's a crucial measure of variability in statistics.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \sigma \) — Standard deviation
• \( f_i \) — Frequency of ith class
• \( x_i \) — Class mark of ith class
• \( \bar{x} \) — Mean of the data

Explanation: The formula calculates how spread out the values are from the mean, weighted by their frequencies.

3. Importance of Standard Deviation Calculation

Details: Standard deviation is essential for understanding data variability, comparing datasets, and making statistical inferences. It's widely used in quality control, finance, and scientific research.

4. Using the Calculator

Tips: Enter class marks and their corresponding frequencies as comma-separated values. Both lists must have the same number of elements.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between population and sample standard deviation?
A: Sample standard deviation uses (n-1) in the denominator (Bessel's correction) to provide an unbiased estimate of the population standard deviation.

Q2: When should I use this formula?
A: Use this when you have grouped frequency data (classes and frequencies) rather than raw individual data points.

Q3: What are class marks?
A: Class marks are the midpoints of class intervals in grouped data. For example, for class 10-20, the class mark is 15.

Q4: What does a high standard deviation indicate?
A: A high standard deviation indicates that data points are spread out widely from the mean, showing high variability.

Q5: Can standard deviation be negative?
A: No, standard deviation is always non-negative as it's derived from squared differences.