A bell-shaped curve that is symmetric about its mean. The normal distribution is the most common statistical distribution because approximate normality arises naturally in many physical, biological, and social measurement situations. Many statistical analyses require that the data come from normally distributed populations. The normal distribution is also known as the Gaussian distribution.
For example, the heights of all adult males residing in the state of Pennsylvania are approximately normally distributed. Therefore, the heights of most men will be close to the mean height of 69 inches. A similar number of men will be just taller and just shorter than 69 inches. Only a few will be much taller or much shorter.
The mean (μ) and the standard deviation (σ) are the two parameters that define the normal distribution. The mean is the peak or center of the bell-shaped curve. The standard deviation determines the spread in the data. Approximately, 68% of observations are within +/- 1 standard deviation of the mean; 95% are within +/- 2 standards deviations of the mean; and 99% are within +/- 3 standard deviations of the mean.
For the height of men in Pennsylvania, the mean height is 69 inches and the standard deviation is 2.5 inches.
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Approximately 68% of Pennsylvania men are between 66.5 (m - 1s) and 71.5 (m + 1s) inches tall. |
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Approximately 95% of Pennsylvania men are between 64 (m - 2s) and 74 (m + 2s) inches tall. |
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Approximately 99% of Pennsylvania men are between 61.5 (m - 3s) and 76.5 (m + 3s) inches tall.
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