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With this information we are able to determine that a salary of $49,000 lies exactly one standard deviation above the mean since $45,000 + $4000 = $49, 000. Acertain segment of the economy has a normally distributed salary, with a mean salary of $45,000 and a standard deviation of $4000. Reconsider an example from the previous section. When a data set is normally distributed we can use a standardized score, called the z-score, to determine the number of standard deviations that a data value is from the mean. Approximately 99.7% of the data items fall within three standard deviations of the mean.Approximately 95% (95.44%) of the data items fall within two standard deviations of the mean.Approximately 68% (68.26%) of the data items fall within one standard deviation of the mean.

Refer to Figure 2 for the visual representation of the 68 – 95 – 99.7 Rule. We have seen that the standard deviation plays an important role in the normal distribution. The area under the curve represents 100% (or 1.00) of the data (or population) and the mean score is 0. The normal curve, also called a bell-shaped curve, is represented in Figure 1. This section will explore how to determine this.Ĭonsider the normal curve which is an idealized representation of a normally distributed population. As an example, a student who has written a college entrance exam may want to know where they placed in comparison to all other students. We will shift gears and explore how to determine where a specific data value lies in relation to all other values. When a set of data values is normally distributed, the 68-95-99.7 Rule can be used to determine the percentage of values that lie one, two or three standard deviations from the mean.