1. What is the Sample Mean?

The sample mean is the average value of a set of numbers. It's calculated by summing all the values in a dataset and dividing by the number of values. The sample mean is a fundamental measure of central tendency in statistics.

2. How Does the Calculator Work?

The calculator uses the sample mean formula:

Where:

• \( x_i \) — Individual values in the sample
• \( n \) — Number of values in the sample
• \( \sum \) — Summation symbol (add all values together)

Explanation: The formula calculates the arithmetic average by dividing the total sum of all values by the count of values.

3. Importance of Sample Mean

Details: The sample mean is crucial in statistics as it provides a single value that represents the center of the data distribution. It's used in hypothesis testing, quality control, and as a basis for many other statistical calculations.

4. Using the Calculator

Tips: Enter numerical values separated by commas (e.g., 5, 8, 12, 6, 9). The calculator will ignore any non-numeric values. At least one valid number is required.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between sample mean and population mean?
A: Sample mean is calculated from a subset (sample) of data, while population mean uses all data points in the population. Sample mean is an estimate of the population mean.

Q2: When is the sample mean not a good measure?
A: For skewed distributions or when outliers are present, the median might be a better measure of central tendency.

Q3: Can the mean be calculated for categorical data?
A: No, the mean requires numerical data. For categorical data, you can calculate mode (most frequent value).

Q4: How does sample size affect the mean?
A: Larger samples tend to provide more reliable estimates of the population mean (law of large numbers).

Q5: What's the relationship between mean, median and mode?
A: In a perfectly normal distribution, all three are equal. Differences between them indicate skewness in the data.