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.)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.2: Exponents And Radicals

Problem 87E

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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 Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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