Home
Back
Sample Mean Formula:
| From: | To: |
The sample mean is a statistic that represents the average value in a sample of data. In probability theory, the sample mean is an unbiased estimator of the population mean, meaning that the expected value of the sample mean equals the population mean.
The calculator uses the fundamental probability principle:
Where:
Explanation: In probability theory, the expected value of the sample mean equals the population mean, making it an unbiased estimator of the population parameter.
Details: Understanding the relationship between sample mean and population mean is crucial for statistical inference, hypothesis testing, and making predictions about population parameters based on sample data.
Tips: Enter the population mean value and sample size. The calculator will show the expected value of the sample mean based on probability theory.
Q1: Why is the sample mean equal to the population mean in probability?
A: This is a fundamental property of probability theory - the sample mean is an unbiased estimator of the population mean, meaning its expected value equals the population mean.
Q2: Does sample size affect the expected value of the sample mean?
A: No, the expected value of the sample mean remains equal to the population mean regardless of sample size. However, larger samples provide more precise estimates.
Q3: What is the difference between sample mean and population mean?
A: The population mean is the true average of the entire population, while the sample mean is the average of a subset (sample) drawn from that population.
Q4: When is the sample mean not a good estimator?
A: When the sample is not representative of the population, or when the population distribution has heavy tails and the sample size is small.
Q5: How does the Central Limit Theorem relate to sample means?
A: The Central Limit Theorem states that the distribution of sample means approaches a normal distribution as sample size increases, regardless of the population distribution.