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The sample mean is the average of the values of a variable in a sample, which is the sum of those values divided by the number of values. Using mathematical notation, if a sample of N observations on variable X is taken from the population, the sample mean is: ¯ = =.
For example, the population mean height is equal to the sum of the heights of every individual—divided by the total number of individuals. The sample mean may differ from the population mean, especially for small samples. The law of large numbers states that the larger the size of the sample, the more likely it is that the sample mean will be ...
For example, the sample mean is an unbiased estimator of the population mean. This means that the expected value of the sample mean equals the true population mean. [1] A descriptive statistic is used to summarize the sample data. A test statistic is used in statistical hypothesis testing. A single statistic can be used for multiple purposes ...
The arithmetic mean (or simply mean or average) of a list of numbers, is the sum of all of the numbers divided by their count.Similarly, the mean of a sample ,, …,, usually denoted by ¯, is the sum of the sampled values divided by the number of items in the sample.
¯ = sample mean of differences d 0 {\displaystyle d_{0}} = hypothesized population mean difference s d {\displaystyle s_{d}} = standard deviation of differences
The sampling distribution of a mean is generated by repeated sampling from the same population and recording of the sample means obtained. This forms a distribution of different means, and this distribution has its own mean and variance .
A "parameter" is to a population as a "statistic" is to a sample; that is to say, a parameter describes the true value calculated from the full population (such as the population mean), whereas a statistic is an estimated measurement of the parameter based on a sample (such as the sample mean).
If the data set is a statistical sample (a subset of the population), it is called the sample mean (which for a data set is denoted as ¯). The arithmetic mean can be similarly defined for vectors in multiple dimensions, not only scalar values; this is often referred to as a centroid.