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Name: The mean value of land and buildings per acre from a sample of farmers
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Description: The mean value of land and buildings per acre from a sample of farmers is $1500, with a standard derivation of $100. The data set has bell-shaped distribution. Using the empirical rule, determine which of the following farms, whose land and building

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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The mean value of land and buildings per acre from a sample of farmers is $1500, with a standard derivation of $100. The data set has bell-shaped distribution. Using the empirical rule, determine which of the following farms, whose land and building values per acre are given, are unusual (more than two standards derivations from the mean). Are any of data values very unusual (more then three standard derivations from the mean)? $1357 $1719 $1316 $1176 $1598 $1491

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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Step 1

Assume, x be the random variable representing the value (in dollars) of land and buildings per acre of farmers, $μ$ be the mean value of data set and $σ$ be the standard deviation of data set.

According to the empirical rule for bell shaped distribution, any data point having values greater than $μ + 2 σ$ or lower than $μ - 2 σ$ can be considered as unusual data point. Also, any data point having values greater than $μ + 3 σ$ or lower than $μ - 3 σ$ can be considered as very unusual data point.

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