Answered: Refer to Table S6.1 - Factors for…

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter11: Data Analysis And Displays

Section: Chapter Questions

Problem 7CR

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Refer to

Table S6.1 - Factors for Computing Control Chart Limits (3 sigma)

for this problem.

Twelve samples, each containing five parts, were taken from a process that produces steel rods at Emmanual Kodzi's factory. The length of each rod in the samples was determined. The results were tabulated and sample means and ranges were computed. The results were:

Sample Sample Mean (in.) Range (in.) Sample Sample Mean (in.) Range (in.)
1 10.604 0.033 7 10.601 0.041
2 10.602 0.041 8 10.605 0.034
3 10.591 0.034 9 10.595 0.027
4 10.604 0.051 10 10.601 0.029
5 10.597 0.031 11 10.603 0.039
6 10.597 0.036 12 10.604 0.047

For the given data, the

x = ? inches (round your response to four decimal places).

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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