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Description: A biologist wished to study the effects of ethanol on sleep time. A sample of 80 rats, matched for age and other characteristics, was selected, and each rat was given an oral injection having a particular concentration of ethanol per body weight. 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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A biologist wished to study the effects of ethanol on sleep time. A sample of 80 rats, matched for age and other characteristics, was selected, and each rat was given an oral injection having a particular concentration of ethanol per body weight. The rapid eye movement (REM) sleep time for each rat was then recorded for a 24-hour period. The results are summarized in the side-by-side boxplots below.

(a) How is the amount of ethanol given related to the median REM sleep time? Explain.
(b) Does the amount of ethanol given affect the variability of REM sleep time? Explain.
(c) What amount of ethanol given leads to the most skewed distribution of sleep times?
(d) Is the distribution of REM sleep times for the rats given 2 g/kg ethanol symmetric, skewed left,
or skewed right?

1 g/kg
2 g/kg
4 g/kg
Ethanol
Time (minutes)
20 30 40 50 60 70 80 90

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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