Monday, March 29, 2021

Normal Distribution or Bell Curve


The bell curve is also known as the normal curve or normal distribution. The bell curve has mathematical properties that allow researchers to draw conclusions about where scores (or data) are located relative to other scores (or data).

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The three measures of central tendency (mode, median, mean) are at the same middle point in a normal curve. The numbers representing the middle of the bell curve divide the distribution in half.

On the x-axis in the normal distribution, the mean is at zero and there are standard deviation units above and below the mean. 

The height of the curve indicates the percentage of scores in that area. You can see that a large percentage of the scores are between 1 and -1 standard deviations. About 68% of scores fall between +1 and -1 standard deviations from the mean. 

Look at the illustration below to see that there are about 34% of the scores in falling one standard deviation above the mean and another 34% in one standard deviation below the mean. Thus, 34% + 34% = 68%.


Example: Intelligence test scores (IQ) appear to be distributed like the normal distribution within each age group. The mean IQ is 100 and one standard deviation is 15 points on most IQ tests. Thus, 68% of people of a similar age have IQ scores between 85 and 115.

Knowing that 100 is the average or mean IQ then we know that half of people taking the test are below average intelligence (as measured by the test) and half are above average intelligence.

Learn more about test scores in Applied Statistics: Concepts for Counselors available at  AMAZON   or   GOOGLE


 The ends of the normal distribution are called tails. Extreme scores are in the tails. Consider the low level of the the distribution at - 2.5 or +2.5 standard deviations. At these points, the curve almost touches the x-axis; however, it never the lines of the curve never quite touch the x-axis.

Only a small percentage of scores is beyond 2.5 standard deviations in either direction. Theoretically, the tails of the curve never touch the baseline. Only a small fraction of a percent of scores is beyond 3 standard deviations.

The picture below illustrates the percentage of scores (or data) within different areas of the curve. For example, on a normally distributed test, 34.1% of scores will fall between the mean and 1 standard deviation above the mean. Because the curve is symmetrical, the same percentage will be between the mean and 1 standard deviation below the mean.

Read more about distributions in Chapter 10 of

Applied Statistics Concepts for Counselors at AMAZON    or    GOOGLE

Related posts/ pages

A-Z list of statistics

Skewed distributions

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