Use Chebyshevs rule and the empirical rule to describe the distribution of this data set. Count the actual number of observations that fall within one, two, and three standard deviations of the mean if the data set and compare these counts with the description of the the data set I developed. T4873763651363311152030910 ns376nary statistics:mn n MeanVariance Std. dev. Std. err.43.42631115 128.66667 28287.667 168.1893820309xxKurtosis ModeMedian Range Min Max Q1 Q3 Sum IQR Unadj. variance Unadj. std. dev. Coef. of var. Skewness31 484 3 487 7 309 1930 302130.71713 1.1532114 -0.19877862 726401.822162.48638

The values are given of size 14. Sample size (n) = 14

Answered: Use Chebyshevs rule and the empirical…

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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Use Chebyshevs rule and the empirical rule to describe the distribution of this data set. Count the actual number of observations that fall within one, two, and three standard deviations of the mean if the data set and compare these counts with the description of the the data set I developed.

ns
376
nary statistics:
mn n Mean
Variance Std. dev. Std. err.
43.426311
15 128.66667 28287.667 168.18938
20
309
xx
Kurtosis Mode
Median Range Min Max Q1 Q3 Sum IQR Unadj. variance Unadj. std. dev. Coef. of var. Skewness
31 484 3 487 7 309 1930 302
130.71713 1.1532114 -0.19877862 7
26401.822
162.48638

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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