A sample mean is the average from a set of data. Sample means are important in that they can give an idea of central tendency-- that is, an idea of the general tendency of a set of numbers. Through statistical analysis using the sample mean, statisticians can calculate items such as standard deviation and variance. Sample mean can be used in settings such as classrooms to determine the average score on a test, or in baseball to determine a player's batting average.
Although the mean is often a very useful number to represent a data set, you might also find other measures of central tendency helpful. For example, the median is the value exactly halfway between the lowest and highest in the dataset. Another measure is the mode. This is the most common value in a dataset. Using the mode will help give a value that is not skewed by a few very high or very low values. In a normal distribution, that is, a perfect bell curve, the mean, median, and mode will all be the same. It is when a distribution is skewed that they differ, and then you need to be careful about what exactly you are looking for and choose your measure accordingly.
Determine the data set. This can be almost anything -- a set of heights, weights, salaries or the amount of grocery bills, for example.
Consider the case of a manager trying to decide whether to place an ad in a local newspaper or a national one for a job opening. To do this, it would be useful to know whether the people working at the company were born nearby or came from far away. If you want to figure out the average distance from your coworkers' birthplaces to the workplace, you'll first collect the data. It could be a list composed of the following distances: 44 miles, 17 miles, 522 miles, 849 miles, 71 miles, 64 miles, 486 miles and 235 miles.
Add together the numbers in the data set.
For the example of distances, you would add 44 + 17 + 522 + 849 + 71 + 64 + 486 + 235, which sum to 2288 miles.
Divide the sum of the data by the number of entries in the data set.
In the example you have eight numbers in your dataset, so you'll divide the sum of 2288 miles by 8, which gives you 286 miles.
Tips
References
Tips
- Although the mean is often a very useful number to represent a data set, you might also find other measures of central tendency helpful. For example, the median is the value exactly halfway between the lowest and highest in the dataset. Another measure is the mode. This is the most common value in a dataset. Using the mode will help give a value that is not skewed by a few very high or very low values. In a normal distribution, that is, a perfect bell curve, the mean, median, and mode will all be the same. It is when a distribution is skewed that they differ, and then you need to be careful about what exactly you are looking for and choose your measure accordingly.
About the Author
Carter McBride started writing in 2007 with CMBA's IP section. He has written for Bureau of National Affairs, Inc and various websites. He received a CALI Award for The Actual Impact of MasterCard's Initial Public Offering in 2008. McBride is an attorney with a Juris Doctor from Case Western Reserve University and a Master of Science in accounting from the University of Connecticut.