Answered: Consider a data set of 15 distinct…

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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Consider a data set of 15 distinct measurements with mean A and median B.

(a) If the highest number were increased, what would be the effect on the median and mean? Explain.

A. The mean would remain the same while the median would increase.

B. Both the mean and median would increase.

C. Both the mean and median would remain the same.

D. The mean would increase while the median would remain the same.

(b) If the highest number were decreased to a value still larger than B, what would be the effect on the median and mean?

A. The mean would decrease while the median would remain the same.

B. Both the mean and median would decrease.

C. Both the mean and median would remain the same.

D. The mean would remain the same while the median would decrease.

A. The mean would decrease while the median would remain the same.

B. Both the mean and median would decrease.

C. Both the mean and median would remain the same.

D. The mean would remain the same while the median would decrease.

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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The median is essentially the 50th percentile, so we can think mean as a balance point.

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