# Measures of average, variation and position

Compare and contrast the measures of average, variation and position

Average

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Average is a measure of central tendency. Measures of central tendency are values that attempt to describe data sets by finding the central position within the given data set. Measures of central tendency are also referred to as measures of central location. Apart from average, the other measures of central tendency include the mode and median. The average, also referred to as the mean is the most well-known and popular measure of central tendency. It is used with both continuous and discrete data, but it is often used with continuous data (Manikandan, 2011).

To compute the average, the sum of all values within a data set is divided by number of values in that data set. The average is a model of a data set and a value that is most common. The average, however, may not be one of the actual values listed in the data set. The importance of the average is that it reduces the error when predicting any value of the data set. That is, it is a value that gives the least amount of error from all the values in the data set (Manikandan, 2011). The average is important when finding variation.

Variation

Variation is a measure of dispersion. In statistics, dispersion describes the manner in which data set is spread out. When the set of data has a large value, values in that set are scattered widely. An example of a data set that is widely scattered is 0, 1, 20, 30, 40, 100. When the set of data has small items, the set is tightly clustered. An example of a data set that has a small value is 1, 2, 2, 3, 3, 4. Apart from variation, other measures of dispersion include standard deviation, average deviation and interquartile range (Turner, 2016).

Variation measures the spread of data in a set. Total variation in a set of data is found by adding the deviation of each value from the average. The average variation (or deviation) is then achieved by dividing the result by the total number of values. Variation of values from the mean is calculated depending on the statistical choice. Unlike in absolute variation, which gets rid of negative values by using absolute values, variance squares the deviations to achieve positive values. Variance is defined as the average of the squared differences from the mean.

Measures of Position

Measures of position are techniques which divide data set into equal groups. For a determination of measures of position to take place, data is sorted from lowest to highest. The various measures of position include quartiles, deciles, standard scores and percentiles. The standard score, also referred to as the z-score, provides the position of a value by identifying its distance from the average, in standard deviation units. A standard score is computed using the standard deviation and the average only. Percentiles, quartiles and deciles are collectively referred to as quantiles. A quantile is a value in which the specified quantity falls below that value. For instance, the 68th percentile is a value in which 68% of data falls below. Also, the third quartile is the value in which ¾ of data falls below (Eisenberger, 2010).

References

Eisenberger, I. (2010). Testing the Mean and Standard Deviation of a Normal Distribution Using Quantiles. Technometrics, 10(4), 781. http://dx.doi.org/10.2307/1267459

Manikandan, S. (2011). Measures of central tendency: The mean. Journal Of Pharmacology And Pharmacotherapeutics, 2(2), 140. http://dx.doi.org/10.4103/0976-500x.81920

Turner, S. (2016). Measures of Dispersion. Collection Management, 2(1), 59-64. http://dx.doi.org/10.1300/j105v02n01_05

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