Answered: The mean value of land and buildings…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 3CYU

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The mean value of land and buildings per acre from a sample of farms is $1300, with a standard deviation of $200. The data set has a bell-shaped distribution. Assume farms in the sample is 74.

(a) Use the empirical rule to estimate the number of farms whose land and building values per acre are between $1100 and $1500.

___farms (Round to the nearest whole number as needed.)

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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(b) If 29 additional farms were sampled, about how many of these additional farms would you expect to have land and building values between $1100 per acre and $1500 per acre?

__farms out of 29 (Round to the nearest whole number as needed.)

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