Answered: The median ACT scores for four-year…

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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Question

The median ACT scores for four-year colleges to follow normal distribution with a mean of 24 points and a standard deviation of 4. We look at the distribution of means of the MidACT variable for samples of 150 colleges at a time. a) using the normal distribution for MidACT, what proportion of colleges should have MidACT of 26 or higher? b) what proportion of samples of 100 colleges would give a sample mean of MidACT of 26 or higher? c) would the results of part a and part b still be appropriate if the distribution of MidACT values for the population of all four-year colleges was actually right-skewed( but still had a mean of 24 and standard deviation of 4)?

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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