How to Interpret the Bell Curve

The bell curve, formally known as the normal distribution function, is a two-dimensional curve in statistics. For data sets that follow a normal distribution, the function relates the frequency of data with different deviations from the mean average. For values that are close to the mean of the data, the frequency (or equivalently, the probability) will be higher. Because the curve is in the shape of a bell, the y-value (frequency) can approach zero but will never reach it. For a true bell curve, the domain is infinite in both directions. The most well-known application of the bell curve relates to analyzing human IQ.

Instructions

    • 1

      Refer to your bell curve or make a quick sketch if one is not provided. Divide the curve into sections with vertical lines at the following positions on the x-axis: at the mean value for the data (for IQ, mean is 100); at +1 and -1 standard deviation from the mean (for IQ, given a standard deviation of 15, this is at 115 and 85); and at +2 and -2 standard deviations from the mean (for IQ, at 130 and 70).

    • 2

      Label the x-axis at these positions with both the data values and the equivalent number of standard deviations in brackets (at the mean value, write 0 in brackets).

    • 3

      Refer to the 68-95-99.7 rule, also known as the empirical rule, which states that for data following a normal curve, 68% of the data population will fall within one standard deviation of the mean, 95% within two standard deviations and 99.7% within three standard deviations. For example, if you shade the area between -1 and +1, 68% of the data will fall within this range (for IQ, 68% of people will have a score between 85 and 115).

    • 4

      Interpret the bell curve to answer any questions you have about the data. You can determine that 68% of your data will fall between the value that is one standard deviation less than the mean and the value that is one standard deviation greater than the mean. You can determine that 34% (half of 68%) will be between the value of the mean and one standard deviation above. You can determine that 0.3% will be either more or less than three standard deviations from the mean.

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