A 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: 381 350 356 360 379 425 323 395 403 373 374 371 364 366 364 326 339 394 393 368 376 359 353 405 331 398 (a) Construct a stem-and-leaf display of the data. (Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.) How does it suggest that the sample mean and median will compare? The display is negatively skewed, so the mean will be greater than the median. The display is reasonably symmetric, so the mean and median will be close. The display is positively skewed, so the mean will be greater than the median. The display is positively skewed, so the median will be greater than the mean. The display is negatively skewed, so the median will be greater than the mean. (b) Calculate the values of the sample mean x and median . [Hint: Σxi = 9626.] (Round your answers to two decimal places.) - x= ? sec ~ x= ? sec (c) By how much could the largest time, currently 425, be increased without affecting the value of the sample median? (Enter ∞ if there is no limit to the amount.) By how much could this value be decreased without affecting the value of the sample median? (Enter ∞ if there is no limit to the amount.)

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 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:

381	350	356	360	379	425	323	395	403
373	374	371	364	366	364	326	339	394
393	368	376	359	353	405	331	398

(a) Construct a stem-and-leaf display of the data. (Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.)

How does it suggest that the sample mean and median will compare?

The display is negatively skewed, so the mean will be greater than the median.

The display is reasonably symmetric, so the mean and median will be close.

The display is positively skewed, so the mean will be greater than the median.

The display is positively skewed, so the median will be greater than the mean.

The display is negatively skewed, so the median will be greater than the mean.

(b) Calculate the values of the sample mean x and median . [Hint: Σx_i = 9626.] (Round your answers to two decimal places.)

x= ? sec

(c) By how much could the largest time, currently 425, be increased without affecting the value of the sample median? (Enter ∞ if there is no limit to the amount.)

By how much could this value be decreased without affecting the value of the sample median? (Enter ∞ if there is no limit to the amount.)

(d) What are the values of x and when the observations are reexpressed in minutes? (Round your answers to two decimal places.)

x= ? min

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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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