Answered: The data below represent US exports (in…

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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The data below represent US exports (in billions of dollars) to 18 countries in 2015

Canada

133.7

Mexico

56.8

Germany

23.5

Taiwan

18.4

Norway

16.6

China

12.0

Australia

12.0

Malaysia

8.5

Japan

67.5

30.9

South Korea

26.6

France

14.4

Brazil

12.7

Belgium

12.5

Italy

8.8

Thailand

7.2

S.A

7.3

Austria

7.3

Find the mean and median.

What is the most appropriate measure of central tendency for this sample? Why?

Find the sum of squares, range, variance, and standard deviation for the sample.

What is the z-score for the UK?

What is the z-score for SA?

What percent of the data falls between Saudi Arabia and Norway?

What raw scores (two scores) correspond to the boundaries of the center 95% of the distribution?

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 data in ascending order is given below;

No.	Country	Exports (x)
1	Thailand	7.2
2	S.A.	7.3
3	Austria	7.3
4	Malaysia	8.5
5	Italy	8.8
6	China	12.0
7	Australia	12.0
8	Belgium	12.5
9	Brazil	12.7
10	France	14.4
11	Norway	16.6
12	Taiwan	18.4
13	Germany	23.5
14	South Korea	26.6
15	UK	30.9
16	Mexico	56.8
17	Japan	67.5
18	Canada	133.7
SUM		476.7

$M e a n = \frac{1}{n} \sum_{i} x_{i} = \frac{476.7}{18} = 26.4833 H e r e n = 18 . T h a t i s n i s e v e n . M e d i a n = \frac{(\frac{n}{2}) t h o b s e r v a t i o n + (\frac{n}{2} + 1) t h o b s e r v a t i o n}{2} = \frac{9 t h o b s e r v a t i o n + 10 t h o b s e r v a t i o n}{2} = \frac{12.7 + 14.4}{2} = 13.55$

The most appropriate measure of central tendency for this sample is median. Since the data is skewed towards the right.

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