Answered: Three randomly selected children are…

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

Three randomly selected children are surveyed. The ages of the children are

and

12.

Assume that samples of size

n=2

are randomly selected with replacement from the population of

and

12.

Listed below are the nine different samples. Complete parts (a) through (d).

2,2

2,4

2,12

4,2

4,4

4,12

12,2

12,4

12,12

a. Find the value of the population median.

enter your response here

(Type an integer or a decimal. Do not round.)

b. Find the median of each of the nine samples, then summarize the sampling distribution of the medians in the format of a table representing the probability distribution of the distinct median values.

Sample Median	Probability
▼ 4.8 2 6.4	enter your response here
▼ 5 3 5.5	enter your response here
▼ 1.2 2.8 4	enter your response here
▼ 10 14 7	enter your response here
▼ 16 13 8	enter your response here
▼ 18 24 12	enter your response here

(Type integers or simplified fractions.)

c. Find the mean of the sampling distribution of the sample median.

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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