A study of all widgets from a factory showed the mean age of widgets to be 22.2 years with a standard deviation of 1.1 years.Are these numbers statistics or parameters? Explain.The numbers are parameters because the numbers were calculated for a sample of widgets and are estimates.The numbers are parameters because the numbers were calculated for all widgets from the factory.The numbers are statistics because the numbers were calculated for a sample of widgets and are estimates.The numbers are statistics because the numbers were calculated for all widgets from the factory.Select the correct label for the numbersThe correct labels for 22.2 months and 1.1 months are:μ = 22.2 months and s = 1.1 monthsxˉx̄ = 22.2 months and σ = 1.1 monthss = 22.2 months and σ = 1.1 monthsxˉx̄ = 22.2 months and s = 1.1 monthsμ = 22.2 months and σ = 1.1 monthsμ = 22.2 months and xˉx̄ = 1.1 months

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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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A study of all widgets from a factory showed the mean age of widgets to be 22.2 years with a standard deviation of 1.1 years.

Are these numbers statistics or parameters? Explain.

The numbers are parameters because the numbers were calculated for a sample of widgets and are estimates.
The numbers are parameters because the numbers were calculated for all widgets from the factory.
The numbers are statistics because the numbers were calculated for a sample of widgets and are estimates.
The numbers are statistics because the numbers were calculated for all widgets from the factory.

Select the correct label for the numbers

The correct labels for 22.2 months and 1.1 months are:

μ = 22.2 months and s = 1.1 months
xˉx̄ = 22.2 months and σ = 1.1 months
s = 22.2 months and σ = 1.1 months
xˉx̄ = 22.2 months and s = 1.1 months
μ = 22.2 months and σ = 1.1 months
μ = 22.2 months and xˉx̄ = 1.1 months

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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A parameter is a descriptive measure that is calculated for the entire population. Generally, we denote parameters using Greek letters, mu for mean and sigma for standard deviation.

A statistic is a descriptive measure that is calculated from the sub-group of a population, called the sample. A sample is usually smaller than the population. The largest possible sample is the population itself.

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