Sampling is used in statistics because you can't possibly ask everyone in the world how old they are in order to find out the average age of all humans. But by getting a representative sample, you can make a pretty accurate estimation of the average age of everyone on the planet.
Another less obvious reason sampling is used is to get rid of bias. If you ask 10 of your friends if they like apples and 9 of them say they do, you can't say that 90% of people like apples. Maybe 90% of your friends, but it's very important to get a sample that accurately represents and reflects the population you are studying.
A statistic and a sample have a relationship similar to that between a population and a parameter. A sample is a subset of a population, while a statistic is a numerical value calculated from that sample, used to estimate the corresponding population parameter. Essentially, a statistic provides insight into the characteristics of a larger group based on the analysis of a smaller, representative portion.
A point estimate is a single value (statistic) used to estimate a population value (parameter)true apex
Statistic
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When the population size is larger than the sample size, the sample statistic is still an estimate of the population parameter, but it may have a larger margin of error due to reduced representativeness. As the sample size increases relative to the population, the sample statistic generally becomes a more accurate reflection of the true population parameter. However, if the sample is randomly selected, the size difference alone does not inherently distort the sample statistic's validity; it's the sampling method that plays a crucial role in accuracy.
σ (sigma)
A statistic and a sample have a relationship similar to that between a population and a parameter. A sample is a subset of a population, while a statistic is a numerical value calculated from that sample, used to estimate the corresponding population parameter. Essentially, a statistic provides insight into the characteristics of a larger group based on the analysis of a smaller, representative portion.
This is called a sample statistic. They are often used to give a general picture of a more specific whole.
the sample standard deviation
sample statistic
No. A statistic is a number describing a characteristic of a sample.
A point estimate is a single value (statistic) used to estimate a population value (parameter)true apex
Statistic
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The relations depend on what measures. The sample mean is an unbiased estimate for the population mean, with maximum likelihood. The sample maximum is a lower bound for the population maximum.
That is the definition of a statistic
You have not defined M, but I will consider it is a statistic of the sample. For an random sample, the expected value of a statistic, will be a closer approximation to the parameter value of the population as the sample size increases. In more mathematical language, the measures of dispersion (standard deviation or variance) from the calculated statistic are expected to decrease as the sample size increases.