# My wife often tells friends that when I walk into one of
# my sections I raise the average age of people in the room 
# by 30 years.  It is a good joke and it reflects how much
# older I am than the age of the students in my class.  
#
# Let us see how much I really do increase the average age.
# First, let us set the ages of all the students.

student_age <- c( 21, 19, 23, 18, 19, 20, 27, 19, 22, 20,
                  16, 20, 19, 33, 28, 17, 19, 20, 24, 17,
                  22, 26, 22, 19, 45, 20, 28, 20, 19, 21)
#  then we can find the average age of those students
mean( student_age )
#  Now we can find the ages of everyone once I enter the room
all_ages <- c( student_age, 75 )
#  what is the average of all 31 people?
mean( all_ages )
# so I raised the average age, but only by 1.70645 years

# Even for a group as small as 30 it is hard to move the 
# the average age by adding just one person to the room.

#  it might be interesting to see what happens
#  to the median ages
median( student_age )
median( all_ages )
#  In this case the median did not change at all.

#  let us just look at the sorted list of ages
sort( all_ages )

# a different question would be "How old would I have 
# to be in order for me to really raise the average
# age of that section by 30 years?" 

# We know that the average age is 22.1 and we get that 
# by dividing the sum of the ages by the number of 
# students.
sum( student_age )
length( student_age )
663/30
# Now, if I want to add one person, so we will have
# 31 people, and I want to have the average of the 31
# people be 22.1+30 = 52.1 then the sum of the 31 ages
# will have to be 31*52.1
31*52.1
#  But the sum of the 30 student ages is only 663.
#  So, my age would have to be 1615.1- 663
1615.1-663
# Thus, If I were 952.1 years old, and I know that may 
# seem correct given my appearance, then when I walk into
# the room I would raise the average age by 30 years!
new_ages <- c(student_age, 952.1)
mean( new_ages )