The following table lists the ages at the time of death for the 38 deceased American presidents from George Washington to Ronald Reagan:Washington 67 Arthur 56J. Adams 90 Cleveland 71Jefferson 83 B. Harrison 67Madison 85 McKinley 58Monroe 73 T. Roosevelt 60J. Q. Adams 80 Taft 72Jackson 78 Wilson 67Van Buren 79 Harding 57W. H. Harrison 68 Coolidge 60Tyler 71 Hoover 90Polk 53 F. D. Roosevelt 63Taylor 65 Truman 88Fillmore 74 Eisenhower 78Pierce 64 Kennedy 46Buchanan 77 L. Johnson 64Lincoln 56 Nixon 81A. Johnson 66 Ford 93Grant 63 Carter 93Hayes 70 Reagan 93Garfield 49a. Before you graph the data, try to visualize the distribution of the ages at death for the presidents. What shape do you think it will have?b. Construct a stem and leaf plot for the data. Describe the shape. Does it surprise you?c. The five youngest presidents at the time of death appear in the lower “tail” of the distribution. Three of the five youngest have one common trait. Identify the five youngest presidents at death. What common trait explains these mea-surements?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
The following table lists the ages at the time of death for the 38 deceased American presidents from George Washington to Ronald Reagan:
Washington 67 Arthur 56
J. Adams 90 Cleveland 71
Jefferson 83 B. Harrison 67
Madison 85 McKinley 58
Monroe 73 T. Roosevelt 60
J. Q. Adams 80 Taft 72
Jackson 78 Wilson 67
Van Buren 79 Harding 57
W. H. Harrison 68 Coolidge 60
Tyler 71 Hoover 90
Polk 53 F. D. Roosevelt 63
Taylor 65 Truman 88
Fillmore 74 Eisenhower 78
Pierce 64 Kennedy 46
Buchanan 77 L. Johnson 64
Lincoln 56 Nixon 81
A. Johnson 66 Ford 93
Grant 63 Carter 93
Hayes 70 Reagan 93
Garfield 49
a. Before you graph the data, try to visualize the distribution of the ages at death for the presidents. What shape do you think it will have?
b. Construct a stem and leaf plot for the data. Describe the shape. Does it surprise you?
c. The five youngest presidents at the time of death appear in the lower “tail” of the distribution. Three of the five youngest have one common trait. Identify the five youngest presidents at death. What common trait explains these mea-surements?
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