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how to calculate data

The value of calculating data is in the data. That’s because the importance of data often comes from the decisions we make with the data.

Before saving the Calculated Metrics check at Data Preview on the right side of the Data Calculations window if the Unit is being displayed. If the Unit is not being displayed, update the Format for the Calculated Metrics at the bottom of the Data Preview. You can choose between Prefixed $, Prefixed £, Prefixed €, Prefixed A$, Prefixed currency, Postfixed currency, Prefixed unit, Postfixed unit, or add a New Custom Format. Learn more about how to add a custom Format here. An important characteristic of any set of data is the variation in the data. In some data sets, the data values are concentrated closely near the mean; in other data sets, the data values are more widely spread out from the mean. The most common measure of variation, or spread, is the standard deviation. The standard deviation is a number that measures how far data values are from their mean. A data value that is two standard deviations from the average is just on the borderline for what many statisticians would consider to be far from the average. Considering data to be far from the mean if it is more than two standard deviations away is more of an approximate “rule of thumb” than a rigid rule. In general, the shape of the distribution of the data affects how much of the data is further away than two standard deviations. (You will learn more about this in later chapters.)

The procedure to calculate the standard deviation depends on whether the numbers are the entire population or are data from a sample. The calculations are similar, but not identical. Therefore the symbol used to represent the standard deviation depends on whether it is calculated from a population or a sample. The lower case letter [latex]s[/latex] represents the sample standard deviation and the Greek letter [latex]σ[/latex] (sigma, lower case) represents the population standard deviation. If the sample has the same characteristics as the population, then [latex]s[/latex] should be a good estimate of [latex]σ[/latex]. The deviations show how spread out the data are about the mean. The data value [latex]11.5[/latex] is farther from the mean than is the data value [latex]11[/latex] which is indicated by the deviations [latex]0.97[/latex] and [latex]0.47[/latex]. A positive deviation occurs when the data value is greater than the mean, whereas a negative deviation occurs when the data value is less than the mean. The deviation is [latex]–1.525[/latex] for the data value nine. If you add the deviations, the sum is always zero. (For Example 1, there are [latex]n = 20[/latex] deviations.) So you cannot simply add the deviations to get the spread of the data. By squaring the deviations, you make them positive numbers, and the sum will also be positive. The variance, then, is the average squared deviation. (Source: courses.lumenlearning.com)