![]() ![]() 99.7% of scores are within 3 standard deviations of the mean.95% of scores are within 2 standard deviations of the mean.68% of scores are within one standard deviation of the mean.Standard normal deviations follow the 68-95-99.7% rule: 99.7 % of the area is within 3 standard deviations of the mean.approximately 95% of the area is within two standard deviations of the mean.68% of the area is within one standard deviation of the mean.are defined by two parameters: the mean and standard deviation.are denser in the center and less dense in the tails.Even though normal distributions can differ in their means and standard deviation, they share some characteristics related to the distribution of scores: It is also known as the bell curve or Gaussian curve. The normal distribution is the most important and commonly used distribution in statistics. So scores in Set B are more dispersed than scores in Set A. In this example, the scores in Set A are 0.82 away from the mean in Set B, scores are 2.65 away from the mean, even though the mean is the same for both sets. In this example, both sets of data have the same mean, but the standard deviation coefficient is different: As mentioned before, a small standard deviation coefficient indicates that scores are close together, whilst a large standard deviation coefficient indicates that scores are far apart. The standard deviation is 1.22.ĭistributions with the same mean can have different standard deviations. To do so, take the square root of the variance. Since we already know the variance, we can use it to calculate the standard deviation. ![]() In the previous section- Variance- we computed the variance of scores on a Statistics test by calculating the distance from the mean for each score,t hen squaring each deviation from the mean, and finally calculating the mean of the squared deviations. Note that the standard deviation is the square root of the variance.Įxample: how to calculate the standard deviation:
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