get the sample mean, sample variance, and sample standard deviation: X P(x) x *P(x) x2 X2P(x)57inches1/222.59353249147.8295 59 inches3/228.04763481474.808459.50inches1/222.707253540.25161.081460inches1/224.4543600327.2461 inches5/2213.86353721845.783361.20 inches3/228.347683745.44510.87862inches1/222.8213844174.90263.2inches1/222.87563994.24181.737963.6 inches1/222.89384044.96184.045764inches1/222.9124096186.36864.8inches1/222.94844199.04191.056365 inches1/222.95754225192.237569 inches1/223.13954761216.6255 = 61.56313 = 3794.594

Given Information: X P(X) X.PX X2 X2.PX 57 122 2.5935 3249 147.8295 59 322 8.0476 3481…

Answered: get the sample mean, sample variance,…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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get the sample mean, sample variance, and sample standard deviation:

X	P(x)	*x P(x)**	x²	X²P(x)
57 inches	1/22	2.5935	3249	147.8295
59 inches	3/22	8.0476	3481	474.8084
59.50 inches	1/22	2.70725	3540.25	161.0814
60 inches	1/22	4.454	3600	327.24
61 inches	5/22	13.8635	3721	845.7833
61.20 inches	3/22	8.34768	3745.44	510.878
62 inches	1/22	2.821	3844	174.902
63.2 inches	1/22	2.8756	3994.24	181.7379
63.6 inches	1/22	2.8938	4044.96	184.0457
64 inches	1/22	2.912	4096	186.368
64.8 inches	1/22	2.9484	4199.04	191.0563
65 inches	1/22	2.9575	4225	192.2375
69 inches	1/22	3.1395	4761	216.6255
		= 61.56313		= 3794.594

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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