Write a set of eight numbers with a mean of 40 and a standard deviation of 0. (Enter your answers as a comma-separated list.) Is there more than one possible set of numbers? Explain. a)There is only one set of numbers with a mean of 40 and a standard deviation of 0 since a mean of 40 implies the numbers have to all be the same. b)There is more than one set of numbers with a mean of 40 and a standard deviation of 0 since there are many sets of numbers with a mean 40, and the standard deviation will always be 0 since the sum of the differences between the numbers and the standard deviation is always 0. c)There is more than one set of numbers with a mean of 40 and a standard deviation of 0 since there are many sets of numbers with a mean 40, and the standard deviation will always be 0 since the sum of the differences between the numbers and the mean is always 0. d)There is more than one set of numbers with a mean of 40 and a standard deviation of 0 since there are many sets of numbers with a mean 40, and the standard deviation will always be 0 if we choose integers for our set of numbers. e)There is only one set of numbers with a mean of 40 and a standard deviation of 0 since a standard deviation of 0 implies the numbers have to all be the same.

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 1GP

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Write a set of eight numbers with a mean of 40 and a standard deviation of 0. (Enter your answers as a comma-separated list.)

Is there more than one possible set of numbers? Explain.

a)There is only one set of numbers with a mean of 40 and a standard deviation of 0 since a mean of 40 implies the numbers have to all be the same.

b)There is more than one set of numbers with a mean of 40 and a standard deviation of 0 since there are many sets of numbers with a mean 40, and the standard deviation will always be 0 since the sum of the differences between the numbers and the standard deviation is always 0.

c)There is more than one set of numbers with a mean of 40 and a standard deviation of 0 since there are many sets of numbers with a mean 40, and the standard deviation will always be 0 since the sum of the differences between the numbers and the mean is always 0.

d)There is more than one set of numbers with a mean of 40 and a standard deviation of 0 since there are many sets of numbers with a mean 40, and the standard deviation will always be 0 if we choose integers for our set of numbers.

e)There is only one set of numbers with a mean of 40 and a standard deviation of 0 since a standard deviation of 0 implies the numbers have to all be the same.

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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