Answered: Suppose an SAT preparation course makes…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 26PFA

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Suppose an SAT preparation course makes the following statement in their advertising brochure: “We asked our graduates to report on their SAT scores before and after taking our course. The mean increase in SAT scores for the 500 graduates who responded was 210 points.”

The mean increase of 210 points is likely just a guess for all graduates of the course.

The mean increase of 210 points is likely less than the actual mean increase for all graduates of the course.

The mean increase of 210 points is likely the actual mean increase for all graduates of the course.

The mean increase of 210 points is likely greater than the actual mean increase for all graduates of the course.

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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