Question at position 16 The simplest measure of variability is the _____.standard deviationvariancecoefficient of variationrangeClear my selection

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BlackTom AI · Accepted Answer

When evaluating measures of variability in data, we start by identifying what each option represents and how it behaves.
Option 1: standard deviation. This statistic measures the average distance of data points from the mean and is widely used because it captures spread in the same units as the data. However, it is not the simplest measure; it involves squaring deviations, summing, averaging, and then taking a square root, which adds computational steps beyond basic counting.
Option 2: variance. Variance is the mean of the squared deviations from the mean. It conveys spread but, like standard deviation, it involves squaring deviations and is expressed in squared units, making interpretation less direct. It is a fundamental concept but not the simplest measure of variability.
Option 3: coefficient of variation. This is a normalized measure of dispersion calculated as the standard deviation divided by the mean. It is useful for comparing variability across datasets with different units or scales, but it is more complex than the simplest measure and requires at least two computations (mean and standard deviation).
Option 4: range. The range is defined as the difference between the maximum and minimum values in the data set. It is the most straightforward and quickest way to gauge spread, requiring only two data points and a subtraction. Because of its simplicity, it is considered the simplest measure of variability.
In summary, standard deviation and variance provide more detailed descriptions of spread but involve more calculations and interpretation challenges; coefficient of variation adds a normalization step; the range offers the most basic, quickest snapshot of how widely data values span.

Question at position 16 The simplest measure of variability is the _____.standard deviationvariancecoefficient of variationrangeClear my selection

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