normal distribution



Bell-shaped symmetrical frequency distribution curve. It is characteristic of many economic, natural, social, and other real world phenomenon (such as IQ scores, height variation within a population, weights of crop yields, variation in quality of manufactured goods) where two or more variables have direct relationship and high predictability (low variation). In normal distribution, extremely-large values and extremely-small values are rare and occur near the tail ends. Most-frequent values are clustered around the mean (which here is same as the median and mode) and fall off smoothly in either side of it. In normal distribution, 68 percent of all values lie within one standard deviation, 95.45 percent within two standard deviations, and 99.8 within three standard deviations (called six sigma in quality control). In other words, only one out of a thousand values will fall outside of six sigma. This distribution is called 'normal' in the sense of 'ideal' or 'standard' against which other distributions may be compared. Also called Gaussian distribution.

Use normal distribution in a sentence

  • Bob and Kevin were recording the body weights of their graduation class and came to the conclusion that their data represented a normal distribution.

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  • The students in my class, being on different levels of intuitive capacity and academic exposure, perform on formative assessments with a variation that follows quite closely a normal distribution, where the majority of the kids perform in the middle range, with less students excelling or failing on opposite ends of the scale.

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  • Often time university professors will grade on a curve to ensure normal distribution of scores among their students and standardize the difficulty of the course.

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