Give an example of a small set of dara for ehich the mean is larger than the third quartile
Transcribed Image Text:The standard deviation remains s =
1 as more Os are added. Use your calculator or
software to find the standard deviation of these numbers, adding extra Os until you get
an incorrect answer. How soon did you go wrong? This demonstrates that calculators
and software cannot handle an arbitrary number of digits correctly.
2.41 You create the data. Create a set of 5 positive numbers (repeats allowed) that
have median 10 and mean 7. What thought process did you use to create your
numbers?
A2 You create the data. Give an example of a small set of data for which the mean is
larger than the third quartile.
Exercises 2.43 to 2.48 ask you to analyze data without having the details outlined for you.
The exercise statements give you the State step of the four-step process. In your work,
follow the Plan, Solve, and Conclude steps as illustrated in Example 2.9.
2.43 Athletes' salaries. In 2007, the Boston Red Sox won the World Series for the
second time in 4 years. Table 2.2 gives the salaries of the 25 players on the Red Sox
World Series roster. Provide the team owner with a full description of the distribution
of salaries and a brief summary of its most important features.
TOBLE ?? Salaries for the 2007 Boston Red Sox World Series team
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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