A learner has the following scores.an ACT composite score of 32an SAT critical writing score of 780an SAT mathematics score of 760What are the z-scores for the data? Round to the nearest hundredth.Recall the following:For the ACT, the mean composite score was 21.0 with a standard deviation of 5.2.For the SAT critical reading score, the mean was 501 with a standard deviation of 112.For the SAT mathematics score, the mean was 516 with a standard deviation of 116.

To find : What are the z-scores for the data?

Answered: A learner has the following scores.…

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 1GP

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A learner has the following scores.

an ACT composite score of 32
an SAT critical writing score of 780
an SAT mathematics score of 760

What are the z-scores for the data? Round to the nearest hundredth.

Recall the following:

For the ACT, the mean composite score was 21.0 with a standard deviation of 5.2.
For the SAT critical reading score, the mean was 501 with a standard deviation of 112.
For the SAT mathematics score, the mean was 516 with a standard deviation of 116.

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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