Answered: Consider the following random sample of…

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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Related questions

Question

Consider the following random sample of data:

12, 27, 28, 14, 23, 7, 8, 3, 110, 19

a) What is the median of the sample data?

Round your response to 2 decimal places.

b) If the outlier is removed, what is the median of the remaining sample data?

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.

Expert Solution

Step 1

Sol:-

a) To find the median of the sample data, we first need to arrange the values in ascending order:

3, 7, 8, 12, 14, 19, 23, 27, 28, 110

The median is the middle value in the sorted list. If the list has an odd number of values, the median is the middle value. If the list has an even number of values, the median is the average of the two middle values. In this case, we have 10 values, so we take the average of the fifth and sixth values:

Median = (14 + 19) / 2 = 16.5

So the median of the sample data is 16.5 rounded to 2 decimal places.