Question

Presidents of the United States. There have been 45 presidents of the US from Washington to Trump. Use data set below that represents the age of each US Presidents upon his first inauguration. ( 57, 61, 57 , 57, 58, 57, 61, 54, 68, 51, 49, 64, 50, 48, 65, 52 56, 46, 54, 49, 51, 47, 55, 55, 54,42,51,56,55,51,54,51,60,62,43,55,56,61,52,69,64,46,54,47,70.) Use 6 classes with the lower limit of 40 for the first class. Use a class widht of 5.

A) Explain why a class size of 5 is a good choice, or if you have preferred to use a different class size. B) What is the range of ages for Presidents at their inauguration, that is the youngest and the oldest? Name them and list their ages. C) What is the mid-range age of Presidents at the inauguration? D) What is the average age of a President upon inauguration? E) What is the standard deviation in age of the Presidents? F) In your opinion, which measure (or measures) of the center best describes the data? Explain your choice. G) If Presidents were within one standard deviation of the mean at the time of their first inauguration, what were these ages? H) What percent of Presidents would you expect to find in this range? I) Which presidents had an unusually low or high age at the time of their inauguration? How do you know?

Answer 1

In order to solve this question I used R software.

R codes and output:

> age=c (57,61,57,57,58,57,61,54,68,51,49,64,50,48,65,52,56,46,54,49,51,47,55,55,54,42,51,56,55,51,54,51,60,62,43,55,56,61,52,69,64,46,54,47,70)
> freq=cut(age,breaks=c(40,45,50,55,60,65,70))
> table(freq)
freq
(40,45] (45,50] (50,55] (55,60] (60,65] (65,70]
2 8 16 9 7 3
> summary(age)
Min. 1st Qu. Median Mean 3rd Qu. Max.
42 51 55 55 58 70
> sd(age)
[1] 6.595453
> hist(age,breaks=c(40,45,50,55,60,65,70))

Que.b

Range = maximum - minimum = 70 - 42 = 28

Que.c

Mid range = (Max + min ) / 2 = (70 + 42 ) / 2 = 56

Que.d

The average age of a President upon inauguration = 55

Que.e

The standard deviation in age of the Presidents =  6.595453

Que.f

Histogram of age 15 10 Frequency 5 40 45 50 55 60 65 70 age

From histogram we see that distribution is positively skewed, hence any measure of central tendency (Mean, Median) work good for it.