Chebyshev’s Rule and the Empirical Rule are rules we use to find intervals where certain amounts of data from a data set is likely to fall.Chebyshev’s Rule can be used for any set of data, and guarantees thatAt least 3/4 of the data (75 %) falls within 2 standard deviations of the mean.At least 8/9 of the data ( 89 %) falls within 3 standard deviations of the mean. Empirical Rule can be used when data is symmetric and bell-shaped, and predicts thatApproximately 95 % of the data falls within 2 standard deviations of the mean.Approximately 99.7 % of the data falls within 3 standard deviations of the mean. Use the above information to answer the following question. Suppose that a set of test scores has sample mean of 67 and sample standard deviation of approximately 6.2. According to Chebyshev’s Rule, at least 75 % of the test scores will fall between Blank 1. Calculate the answer by read surrounding text. and Blank 2. Calculate the answer by read surrounding text. . Do NOT round your answers. Be sure to give the lower value first, followed by the higher value.

Answered: Chebyshev’s Rule and the Empirical Rule…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Chebyshev’s Rule and the Empirical Rule are rules we use to find intervals where certain amounts of data from a data set is likely to fall.

Chebyshev’s Rule can be used for any set of data, and guarantees that

At least 3/4 of the data (75 %) falls within 2 standard deviations of the mean.
At least 8/9 of the data ( 89 %) falls within 3 standard deviations of the mean.

Empirical Rule can be used when data is symmetric and bell-shaped, and predicts that

Approximately 95 % of the data falls within 2 standard deviations of the mean.
Approximately 99.7 % of the data falls within 3 standard deviations of the mean.

Use the above information to answer the following question.

Suppose that a set of test scores has sample mean of 67 and sample standard deviation of approximately 6.2.

According to Chebyshev’s Rule, at least 75 % of the test scores will fall between Blank 1. Calculate the answer by read surrounding text. and Blank 2. Calculate the answer by read surrounding text. .

Do NOT round your answers. Be sure to give the lower value first, followed by the higher value.

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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