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The standard deviation, SD is most widely used measure of dispersion around Mean. It indicates the slope of distributed curve on either side of the mean. According to the nature of dispersal of data, slope could be either gentle or steep. A high SD indicates gentle slope, widely scattered around mean and higher range; while, converse is true, when SD is less. Based on this description, it can be presumed that first set of data will have smaller SD than that of the second set. A normally distributed curve slopes alike on either side of the mean as shown here. This aside, for normally distributed data, mean, median and mode, all coincide.
The variance of a set of data is the average of the square of the difference in value of a datum from the mean:
This has the disadvantage of being measured in the square of the units of the data. The standard deviation is the square root of the variance:
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Statcato is a free, portable, java based statistical analysis software for Windows. In this software, you can find out various statistics, plot graphs to visualize the relationship between variables, evaluate mathematical functions, calculate probability distribution, p-values, etc. In this software, you can enter data in the Data window that has a spreadsheet-like interface and perform all. SPSS is one of the most popular softwares for statistical computing. However, the interpretation of the results depends on the level of knowledge of the user. Note: This is an older version of SPSS, you can try the latest version of SPSS for free after creating an account. We also recommend that you consider a free alternative for this software.
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This formula with denominator 'n' indicates SD of entire population. However, for all practical purposes, we deal with 'samples' only, and in such case, denominator 'n' is replaced by (n-1) to account for limited length of data. Excel formula to estimate this parameter is =stdev(Range of data). Here, for two sets of data, SD computed is 1.58 & 21 respectively, which is consistent with our presumption made earlier.