Answered: on time (sec) to complete the escape…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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Question

sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the accompanying data
on time (sec) to complete the escape (“Oxygen
Consumption and Ventilation During Escape from an
Offshore Platform,” Ergonomics, 1997: 281–292):
389 356 359 363 375 424 325 394 402
373 373 370 364 366 364 325 339 393
392 369 374 359 356 403 334 397

a. Construct a stem-and-leaf display of the data. How
does it suggest that the sample mean and median will
compare?

b. Calculate the values of the sample mean and median.
[Hint: oxi 5 9638.]

c. By how much could the largest time, currently 424,
be increased without affecting the value of the sample median? By how much could this value be
decreased without affecting the value of the sample
median?

d. What are the values of x and ,x when the observations are reexpressed in minutes?

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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