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The expected value of a random variable. Arithmetic average of a sample.

Arithmetic Mean Average

An average calculated by adding the value of the points in a data set and dividing the sum by the number of data points. For example, suppose one wishes to calculate the average income of a country with exactly five people in it, and their incomes are $25,000, $26,000, $43,000, $70,000, and $72,000. It is calculated as:

($25,000 + $26,000 + $43,000 + $70,000 + $72,000) / 5 = $47,200.

A limitation to the arithmetic mean average is that it can be overly affected by extremes in either direction. For example, if one of the five persons in the country earns $100 billion per year, the arithmetic mean average income would be in the billions and would not accurately count the other four citizens. For this reason, many analysts use the median in conjunction with the arithmetic mean average. The arithmetic mean average is also called simply the mean.


The average of a set of numbers.Contrast with median,which is the middle figure in a set of numbers,and mode,which is the value that appears most often in a set of numbers.

Example: A survey of home values in a neighborhood of nine houses obtained the following values:

The mean, or average, is the total of all values divided by 9, or $143,044.The median is the middle number when the numbers are all arranged from highest to lowest,which would be house 5, or $139,850.The mode is $139,000,because it is the number that appears most often.

References in periodicals archive ?
After a short explanation of x-bar and R control charts, we discuss each of the above functions.
PowerWay SPC9000 is Windows-based SPC software offering a variety of statistical-analysis and charting options - including X-bar, range, sigma, individual and moving-range histograms, Pareto, P, C, U, NP, and summary screens.
The x-bar chart monitors the average of a process or product characteristic across time (Figure 3).
Data is displayed in X-bar, R, or histogram chart form, with as many as eight process variables viewed at a time on a multi-windowed display.
2) Control-chart analysis with X-bar, R, and Sigma charts, histograms, and data list of measured values, lot variables, lot mean, and standard deviation.
False SPC assumptions manifest themselves in an over-reliance on x-bar and R-charts.
SPC data (trend/run time, X-bar and R, histogram and scatter diagrams), as well as production data available in graphics and text.
It takes a limited number of process data points, compares them with preset high and low limits, and then displays X-bar and R charts that tell whether a process is "in control.
Traditional X-bar and R charts, van der Veen says, are insensitive and inefficient in monitoring individual cavities in a multicavity mold.
The Boy 50M Mipronic-Plus model also has new SPC displays of X-Bar and R charts for 19 different parameters--optionally expandable to 52.
Collected data are sorted according to tested property, mold number and time; and X-bar and R charts are displayed on a computer screen.
Data in ControlView can be viewed on SPC charts in a real-time mode in traditional X-bar and R, Histogram, and Pareto charts; saved for long-term historical analysis; and mathematically manipulated as input data for alarm checking, process changes, machine status, production reports and other purposes.