Notation (Example 3) The city of San Francisco provides an open data set of commercial building energy use. Each row of the data set represents a commercial building. A sample of 100 buildings from the data set had a mean floor area of 32,470 square feet. Of the sample, 28 % were office buildings. a. What is the correct notation for the value 32,470? b. What is the correct notation for the value 28 % ?
Notation (Example 3) The city of San Francisco provides an open data set of commercial building energy use. Each row of the data set represents a commercial building. A sample of 100 buildings from the data set had a mean floor area of 32,470 square feet. Of the sample, 28 % were office buildings. a. What is the correct notation for the value 32,470? b. What is the correct notation for the value 28 % ?
Solution Summary: The author states the correct notation for the value 32,470, which is the mean of 100 buildings from the data set.
Notation (Example 3) The city of San Francisco provides an open data set of commercial building energy use. Each row of the data set represents a commercial building. A sample of 100 buildings from the data set had a mean floor area of 32,470 square feet. Of the sample,
28
%
were office buildings.
a. What is the correct notation for the value 32,470?
b. What is the correct notation for the value
28
%
?
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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Part (b)
Draw a scatter plot of the ordered pairs.
N
Life
Expectancy
Life
Expectancy
80
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50
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10
Year of
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1970 1990
2010 Birth
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Life
Expectancy
Part (c)
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1950
1970 1990
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Year of
2010 Birth
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1950 1970 1990
2010 Birth
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Expectancy
Ox
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