Which statements accurately describe normal distributions? Select all that apply.In a normal distribution, it is highly likely that almost all values fall within 3 standard deviations of the mean. When graphed, a normal distribution closely resembles a linear graph. In a normal distribution, the data that is most common is close to the mean, and the data becomes less common as you move away from the mean. Data within 1 standard deviation of the mean accounts for approximately 4% of the data set.

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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 24PFA

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Which statements accurately describe normal distributions? Select all that apply.

In a normal distribution, it is highly likely that almost all values fall within 3 standard deviations of the mean.
	When graphed, a normal distribution closely resembles a linear graph.
	In a normal distribution, the data that is most common is close to the mean, and the data becomes less common as you move away from the mean.
	Data within 1 standard deviation of the mean accounts for approximately 4% of the data set.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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