The arithmetic mean is the average of a group of numbers and is computed by summing all numbers and dividing by the number of numbers. The arithmetic mean is also usually just called the mean.

In these lessons, we will distinguish between the population mean and sample mean.

Related Topics: More Statistics Lessons

A population is a collection of persons, objects or items of interest.

A sample is a portion of the whole and, if properly taken, is representative of the whole.

The population mean is represented by the Greek letter *mu *. It is given by the formula

The capital Greek letter sigma is commonly used in mathematics to represent a summation of all the numbers in a grouping.
*N* is the number of terms in the population.

The sample mean is represented by (x bar). It is given by the formula

*n *is the number of terms in the sample.

The following video shows how to find the sample mean and highlights the difference between the mean of a sample and the mean of a population. In statistics, we use data from a random sample to represent the population at large. From that sample mean, we can infer things about the population mean. We infer the population mean from the sample mean because we are not able to collect the data from the entire population.

Sample Mean is the mean of sample values collected.

Population Mean is the mean of all the values in the population.

If the sample is random and sample size is large then the sample mean would be a good estimate of the population mean.

A point estimate is the value of a statistic that estimates the value of a parameter. For example, the sample mean is a point estimate of the population mean.

Example:

Pennies minted after 1982 are made from 97.5% zinc and 2.5% copper. The following data represent the weights (in grams) of 17 randomly selected pennies minted after 1982.

2.46, 2.47, 2.49, 2.48, 2.50, 2.44, 2.46, 2.45, 2.49, 2.47, 2.45, 2.46, 2.45, 2.46, 2.47, 2.44, 2.45

Treat the data as a simple random sample. Estimate the population mean weight of pennies minted after 1982.

The arithmetic mean is a single value meant to "sum up" a data set.

To calculate the mean, add up all the values and divide by the number of values.

There are two types of arithmetic mean: population mean and sample mean.

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