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MBA London Guide Free - Simple - Professional MBA Advice! Understanding the Basics of Standard Deviation If you would like to receive the full article please email us at [email protected] 1 STANDARD DEVIATION Standard deviation is the square root of variance and is the most commonly used measure of dispersion. The standard deviation represents the average amount by which the values in the distribution deviate from the mean. When sufficient large amount of data is used, the patterns of deviations from the mean will be spread symmetrically on either side and if the class interval are small enough the resultant frequency distribution curve may look like a bell shaped curve. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values. In other words, standard deviation is a statistic that tells you how tightly all the various observations are spread around the mean in a set of data. When the observations are pretty tightly bunched together and the bell-shaped curve is steep, the standard deviation is small. When the observations are spread apart and the bell curve is relatively flat, that implies a relatively large standard deviation. The identical distribution is the normal distribution where the bell-shaped curve is formed. Graphically the normal distribution is presented in figure 1 Figure 1: Normal distribution 2 In a normal distribution: • Approximately 2/3 or 68,26% of the observations will be within 1 standard deviation either side of the mean • Approximately 95,5% of all the observations will be within 2 standard deviations either side of the mean • Approximately 99,75% of all the observations will be within 3 standard deviations either side of the mean As a simple example we can examine the average height for adult men in a small town which is estimated at 178 cm, with a standard deviation of around 8cm. This means that most men (about 68 percent, assuming a normal distribution have a height within 8cm of the mean (170–185 cm) – one standard deviation, whereas almost all men (about 95%) have a height within 16 cm of the mean 162–194 cm – 2 standard deviations. If the standard deviation were zero, then all men would be exactly 178 cm high. If the standard deviation was higher then there would be higher variance, namely if the standard deviation were 51 cm, then men would have much more variable heights, with a typical range of about 127 to 229 cm. If this curve was flatter and more spread out, the standard deviation would have to be larger in order to account for those 68 percent or so of the people. The formula for standard deviation (SD) is SD= | ̅| where Σ means "sum of", x is a value in the data set, x is the mean of the data set, and n is the number of data points (sample). 3