Find out the population mean of the quantity as it is mostly given and denoted by µ, if not given; calculate it by adding all the sample observations and dividing it by the number of trials. Denote the numerical sample observations collected randomly from the population by the random variables x1, x2, x3 …, xn where n represents the number of numerical observations.
Formulate a table on spreadsheet software with each trial recorded on a separate row on the vertical axis and sample observations denoted by x1, x2 each taking a column on the horizontal axis, and the last column left blank for the sample mean value. Record the initial values collected from the first observations in their respective place on the table, leaving the column for the sample mean on each row blank.
Repeat the sampling experiment and pick another set of numerical observation denoted by x1, x2 from the population sample set and record them on their respective places on the table. Ensure the number of samples is equal in all the trials for precision, that is if n is equal to 8 in the first observations, then this should be replicated in all the trials. Record this under trial No. 2 on the vertical axis.
Continue randomly picking other sets of observed numerical values from the sample data and recording them under the random variables x1, x2, x3 and the number of trials, as more observations help in increasing the accuracy and precision of the sample mean of the data.
Calculate the sample mean from each of the trials, and write it down at the blank column marked "Sample Mean" at the end of every row. Calculate the average mean of all sample means derived from all the trials as they will have varied answers. If the average obtained is the same as the true population mean denoted by µ, then the sample mean is an unbiased estimator of the population mean.