Answered: What are the big corporations doing…

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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What are the big corporations doing with their wealth? One way to answer this question is to examine profits as percentage of assets. A random sample of 50 Fortune 500 companies gave the following information. (Source: Based on information from Fortune 500, Vol. 135, No. 8.) Estimate the sample mean, sample variance, and sample standard deviation for profit as percentage of assets. (Enter your answers to one decimal place.)

find mean

find s²

Profit as percentage of assets
Number of companies
8.6-12.5
12.6-16.5
16.6-20.5
20.6-24.5
24.6-28.5
14
20
6.
5

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 + ...

Expert Solution

Step 1

Arithmetic mean ( $x$ ) is given as,

$x = \frac{1}{n} {\sum f_{i} x_{i}}_{i = 1}^{5} w h e r e, n i s t h e t o t a l n u m b e r o f s a m p l e o b s e r v a t i o n s . f i s t h e f r e q u e n c y .$

For a given frequency distribution, the standard deviation is written as

$σ^{} = \sqrt{\frac{1}{n} \sum_{i} f_{i} (x_{i} - x})^{2}$

_{The mean square deviation is given as,}

_{$s^{2} = \sqrt{\frac{1}{n} \sum_{i} f_{i} (x_{i} - A})^{2} w h e r e, A i s a n a r b i t r a r y n u m b e r .$}

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