Overview: What Is the Normal Curve?
The normal curve is a frequency distribution with special statistical properties. The best-known application of the normal curve is the distribution of intelligence as measured by tests such as the Stanford-Binet, but there are other examples that are close to the normal curve in human and animal behavior. Biologists, other scientists, and mathematicians try to make it scary by calling it a “Gaussian distribution”. To social scientists and educators, it’s nothing but the normal curve.
What Does the Normal Curve Look Like?
The normal curve is a symmetrical distribution of scores with the mean (the average of all scores), the median (the point at which exactly half of all scores are below and the other half of scores are above), and the mode (the most frequent score) are equal. The further scores get away from the mean, the closer they get to the baseline, but they never touch, even if the score is infinitely far away from the mean. That is a property of the normal curve called “asymptotic.” It is also a continuous curve.
Normal Is a Statistical Artifact
The normal curve itself is a theoretical distribution that first came from mathematicians interested in probability and observational errors, and Gauss was one of those mathematicians who developed it. Scores in real life, such as measurements on IQ tests, ability scores, and the like, follow the normal curve closely, but do not fall exactly on the normal curve. The mode is the most frequently occurring score in the distribution by definition, and a statistical artifact is a fancy way of saying that the scores follow a certain pattern.
What’s So Special about It?
The relative frequencies of scores that are in an approximate normal distribution fall under specific percentages, and no matter what is being measured, if those values follow a normal distribution, those percentages will hold true. Statisticians call the measurement of the distance away from the mean the standard deviation, and about 68% of scores will fall within one standard deviation on either side of the mean. Just a little over 95 % will fall within two standard deviations on either side of the mean, and just over 99% will fall within three standard deviation on either side of the mean. Because the tails never touch the X-axis, that’s as close as it gets.
Using the Normal Curve in Research
The mathematical properties of the normal curve make statistics easier to apply in research when the values that are obtained from observations fall close to the normal curve. There are extensive statistical tables that describe the exact location of values on the normal curve. In addition, because the normal curve was originally developed around probabilities, it is possible to determine how likely something will happen, such as winning the lottery.
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