Answered: Advil and Motrin IB produce the same…

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 8CR

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Advil and Motrin IB produce the same headache relief medication with the active ingredient ibuprofen. Each pill
should contain 200 mg of ibuprofen. A health agency obtains a sample of ten tablets from both manufacturers and measures
how much ibuprofen each pill actually contains.
Number of milligrams measured
Advil 199.25 198.50 200.10 200.75 201.00 198.00 200.10 199.00 201.10 202.20
Motrin IB 205.00 195.80 195.20 203.20 205.80 194.40 204.60 194.60 207.20 194.20
(a) Verify on your calculator that each sample has a mean value of 200 mg.
(b) What is the range of each sample?
(c) However, based on the given sample values, which company would you prefer to buy from? Justify your answer with statistical
reasoning. (Hint: argue using standard deviation and explain why this is desirable in this situation)

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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