Answered: In 2012, the Washington Nationals had…

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

In 2012, the Washington Nationals had the best record in
baseball with 98 wins. The Houston Astros had the worstrecord with 107 losses. To win, a team needs to score
runs. Here are the summary statistics for the runs scored
for hitters on each team (excluding pitchers and players
with fewer than 50 at bats).

a) Construct parallel boxplots for the runs scored. (Note:
the two best hitters for the Astros were Jose Altuve
with 80 runs and Justin Maxwell with 46 runs.)
b) Compare the distributions of runs scored.

c) Explain why the difference in means for these distri-
butions is so much larger than the difference in the

medians.

Column n Mean Variance StdDev StdErr Med Range Min Max Q1 Q3
NatRuns 17 40.7058 1021.22 31.9565 7.7506 25 92 6 98 15 72
AstrosRuns 24 23.5833 317.731 17.8250 3.6385 22 78 2 80 9.5 35

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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