Most probably not. But it should be close to the population mean if various conditions are met:
For example, the population should consist of independent, [nearly] identically distributed variables, the sample is not systematically biased (it does not have to be completely random).
The sample mean is an unbiased estimator of the population mean because the average of all the possible sample means of size n is equal to the population mean.
True.
The population mean is the mean value of the entire population. Contrast this with sample mean, which is the mean value of a sample of the population.
With a good sample, the sample mean gets closer to the population mean.
That the key characteristics of the population are reflected in the sample.
The sample mean is an unbiased estimator of the population mean because the average of all the possible sample means of size n is equal to the population mean.
Yes, the sample mean is an unbiased estimator of the population mean. This means that, on average, the sample mean will equal the true population mean when taken from a large number of random samples. In other words, as the sample size increases, the expected value of the sample mean converges to the population mean, making it a reliable estimator in statistical analysis.
True.
Provided the samples are independent, the Central Limit Theorem will ensure that the sample means will be distributed approximately normally with mean equal to the population mean.
The sample is not a perfect representation of the population.
The standard deviation of the sample means is called the standard error of the mean (SEM). It quantifies the variability of sample means around the population mean and is calculated by dividing the population standard deviation by the square root of the sample size. The SEM decreases as the sample size increases, reflecting improved estimates of the population mean with larger samples.
It means that the every element in a population has an equal chance of being selected to be in the sample which is studied. Equivalently, in considering a sample of a particular size, every possible sample of that size has the same chance of being selected.
The population mean is the mean value of the entire population. Contrast this with sample mean, which is the mean value of a sample of the population.
It means you can take a measure of the variance of the sample and expect that result to be consistent for the entire population, and the sample is a valid representation for/of the population and does not influence that measure of the population.
No, the sample mean and sample proportion are not called population parameters; they are referred to as sample statistics. Population parameters are fixed values that describe a characteristic of the entire population, such as the population mean or population proportion. Sample statistics are estimates derived from a sample and are used to infer about the corresponding population parameters.
It means that every member of the population has the same probability of being included in the sample.
The same basic formula is used to calculate the sample or population mean. The sample mean is x bar and the population mean is mu. Add all the values in the sample or population and divide by the number of data values.