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Chief Justices The following data represent the ages of
Chapter 3, Problem 3RE(choose chapter or problem)
The following data represent the ages of chief justices of the U.S. Supreme Court when they were appointed.
\(\begin{array}{|c|c|} \hline \text { Justice } & \text { Age } \\ \hline \text { John Jay } & 44 \\ \hline \text { John Rutledge } & 56 \\ \hline \text { Oliver Ellsworth } & 51 \\ \hline \text { John Marshall } & 46 \\ \hline \text { Roger B. Taney } & 59 \\ \hline \text { Salmon P. Chase } & 56 \\ \hline \text { Morrison R. Waite } & 58 \\ \hline \text { Melville W. Fuller } & 55 \\ \hline \text { Edward D. White } & 65 \\ \hline \text { William H. Taft } & 64 \\ \hline \text { Charles E. Hughes } & 68 \\ \hline \text { Harlan F. Stone } & 69 \\ \hline \text { Frederick M. Vinson } & 56 \\ \hline \text { Earl Warren } & 62 \\ \hline \text { Warren E. Burger } & 62 \\ \hline \text { William H. Rehnquist } & 62 \\ \hline \text { John G. Roberts } & 50 \\ \hline \end{array}\)
Source: Information Please Almanac
(a) Determine the population mean, median, and mode ages.
(b) Determine the range and population standard deviation ages.
(c) Obtain two simple random samples of size 4, and determine the sample mean and sample standard deviation ages.
Questions & Answers
QUESTION:
The following data represent the ages of chief justices of the U.S. Supreme Court when they were appointed.
\(\begin{array}{|c|c|} \hline \text { Justice } & \text { Age } \\ \hline \text { John Jay } & 44 \\ \hline \text { John Rutledge } & 56 \\ \hline \text { Oliver Ellsworth } & 51 \\ \hline \text { John Marshall } & 46 \\ \hline \text { Roger B. Taney } & 59 \\ \hline \text { Salmon P. Chase } & 56 \\ \hline \text { Morrison R. Waite } & 58 \\ \hline \text { Melville W. Fuller } & 55 \\ \hline \text { Edward D. White } & 65 \\ \hline \text { William H. Taft } & 64 \\ \hline \text { Charles E. Hughes } & 68 \\ \hline \text { Harlan F. Stone } & 69 \\ \hline \text { Frederick M. Vinson } & 56 \\ \hline \text { Earl Warren } & 62 \\ \hline \text { Warren E. Burger } & 62 \\ \hline \text { William H. Rehnquist } & 62 \\ \hline \text { John G. Roberts } & 50 \\ \hline \end{array}\)
Source: Information Please Almanac
(a) Determine the population mean, median, and mode ages.
(b) Determine the range and population standard deviation ages.
(c) Obtain two simple random samples of size 4, and determine the sample mean and sample standard deviation ages.
ANSWER:Step 1 of 2
(a) The arithmetic mean of a variable is computed by adding all the values of the variable in the data set and dividing by the number of observations. The population arithmetic mean, \(\mu\), is computed using all the individuals in a population, ie;
\(\begin{array}{l} \mu=\frac{\sum x_{i}}{N} \\ \mid m u=\frac{44+56+51+46+\ldots \ldots+50}{17}=\frac{983}{17}=57.82 \end{array}\)
The median of a variable is the value that lies in the middle of the data when arranged in ascending order. The number of observations is odd, then the median is the data value exactly in the middle of the data set, ie;
Median, M = 58
The mode of a variable is the most frequent observation of the variable that occurs in the data set. The given data set contains two modes 56 and 62. The data is bimodal.