Standard Deviation and Coefficient of Variation: Measures of Absolute and Relative Dispersion
The standard deviation measures how far the mean is from the mean, while the coefficient of variation measures the ratio of the standard deviation to the mean. The deviation is an absolute value, while the coefficient is relative (Mishra et al., 2019). These indicators are equally important for various purposes of sample analysis. Table 1 shows two examples of such samples with different scatter, for which descriptive statistics are also calculated.
Table 1. Two Data Sets and Descriptive Statistics
Determining the More Informative Measure of Variability: Standard Deviation vs. Coefficient of Variation
In the second sample, the standard deviation is more significant since the ranking of possible data values is more comprehensive, while the variance of the first sample is more diminutive. At the same time, the coefficient of variation shows less variability in the second sample despite the greater scatter.
Suppose these samples reflect marks for different testing systems in two educational classes. In that case, the second class is more consistent in knowledge without a large gap between excellent and lagging students. At the same time, the grading system for the first test assumes a generally smaller spread of data according to the criteria, which, nevertheless, does not prevent the class from being quite different in terms of student performance. Accordingly, according to this example, if it is necessary to know how substantial the gaps are in the relative terms between the abilities and knowledge of students in the class, then one should refer to the coefficient of variation. At the same time, the actual absolute spread in the estimates will already show the standard deviation.
Understanding Excel’s QUARTILE.EXC Function: A Comparison with Textbook Quartile Calculation Methods
In addition, Table 1 presents the quartiles for these samples. Excel offers a calculation using the formula: where xis the quartile index calculated by the formula x=(n-1)p, n is the number of elements in the sample, i is the index of the element in the sample, and Ai is its actual value (Grech, 2018). In the student textbook and the lecture, a more understandable version of the calculation of the first and third quartiles is proposed, which are the median of the lower half of the data set in the first case and the upper half in the second. The Excel calculation formula is more complex but easier to automate, without the need to calculate intermediate values in the form of averages and sort the selection, which will take more time in machine language.
References
Grech, V. (2018). WASP (Write a Scientific Paper) using Excel–5: Quartiles and standard deviation. Early Human Development, 118, 56-60. Web.
Mishra, P., Pandey, C. M., Singh, U., Gupta, A., Sahu, C., & Keshri, A. (2019). Descriptive statistics and normality tests for statistical data. Annals of Cardiac Anaesthesia, 22(1), 67. Web.
Loading...
