Answered: Using the medians in the table, is the…

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 ages of the 5 officers for a school club are 18, 18, 17, 16, and 15. The median of the ages of the officers is 17.0. The table displays all possible samples of size 2 and the corresponding median for each sample.

Using the medians in the table, is the sample median an unbiased estimator?

Yes, 50% of the sample medians are 17 or more, and 50% are below.

Yes, the mean of the sample medians is 16.8, which is the same as the mean age of the officers.

No, the mean of the sample medians is 16.8, which is not the same as the median age of the officers.

No, the median of the sample medians is 16.75, which is not the same as the median age of the officers.

Sample n = 2
Sample Median
18, 18
18
18, 17
17.5
18, 17
17.5
18, 16
18, 15
16.5
18, 15
16.5
17, 16
16.5
16, 15
15.5
18, 16
17, 15
17
17
16

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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