iit scholarship weekend average talk, 2017 february 9
TRANSCRIPT
How to Compute the Average
Fred J. HickernellProfessor and Department Chair
Department of Applied [email protected]
Welcome, future Illinois Tech students, family, and friends!
February 9, 2017 1/10
How to Compute the AverageI already know how . . .
Fred J. HickernellProfessor and Department Chair
Department of Applied [email protected]
Welcome, future Illinois Tech students, family, and friends!
February 9, 2017 1/10
How to Compute the AverageI already know how . . . So that’s an average too . . .
Fred J. HickernellProfessor and Department Chair
Department of Applied [email protected]
Welcome, future Illinois Tech students, family, and friends!
February 9, 2017 1/10
How to Compute the AverageI already know how . . . So that’s an average too . . .
This is not trivial, but it seems fun!
Fred J. HickernellProfessor and Department Chair
Department of Applied [email protected]
Welcome, future Illinois Tech students, family, and friends!
February 9, 2017 1/10
Average Travel Speed Average for a Large Population Financial Risk What I Like About Math
How fast are you traveling on average?
You drive
40 mph for 1 hour, then60 mph for 1 hour.
Your average speed is?
Fred J. Hickernell, [email protected] • Average • 2/9/17 2/10
Average Travel Speed Average for a Large Population Financial Risk What I Like About Math
How fast are you traveling on average?
You drive
40 mph for 1 hour, then60 mph for 1 hour.
Your average speed is?
average speed =total distancetotal time
=40 miles+ 60 miles
1 hour+ 1 hour
=100 miles2 hours
= 50 mph
Fred J. Hickernell, [email protected] • Average • 2/9/17 2/10
Average Travel Speed Average for a Large Population Financial Risk What I Like About Math
How fast are you traveling on average?
You drive
40 mph for 1 hour, then60 mph for 1 hour.
Your average speed is?
average speed =total distancetotal time
=40 miles+ 60 miles
1 hour+ 1 hour
=12(40 + 60) mph (the average)
= 50 mph
Fred J. Hickernell, [email protected] • Average • 2/9/17 2/10
Average Travel Speed Average for a Large Population Financial Risk What I Like About Math
How fast are you traveling on average?
You drive
40 mph for //1 //////hour 10 miles, then60 mph for //1 //////hour 10 miles.
Your average speed is?
Fred J. Hickernell, [email protected] • Average • 2/9/17 2/10
Average Travel Speed Average for a Large Population Financial Risk What I Like About Math
How fast are you traveling on average?
You drive
40 mph for //1 //////hour 10 miles, then60 mph for //1 //////hour 10 miles.
Your average speed is?
average speed =total distancetotal time
=10 miles+ 10 miles
1040 hour+ 10
60 hour
=20 miles
512 hour
= 48 mphFred J. Hickernell, [email protected] • Average • 2/9/17 2/10
Average Travel Speed Average for a Large Population Financial Risk What I Like About Math
How fast are you traveling on average?
You drive
40 mph for //1 //////hour 10 miles, then60 mph for //1 //////hour 10 miles.
Your average speed is?
average speed =total distancetotal time
=10 miles+ 10 miles
1040 hour+ 10
60 hour
=20 miles
512 hour
= 48 mph ă 50 mphFred J. Hickernell, [email protected] • Average • 2/9/17 2/10
Average Travel Speed Average for a Large Population Financial Risk What I Like About Math
How fast are you traveling on average?
You drive
40 mph for //1 //////hour 10 miles, then60 mph for //1 //////hour 10 miles.
Your average speed is?
average speed =total distancetotal time
=10 miles+ 10 miles
1040 hour+ 10
60 hour
=1
12[ 1
40 + 160] mph (harmonic average, still an average)
= 48 mphFred J. Hickernell, [email protected] • Average • 2/9/17 2/10
Average Travel Speed Average for a Large Population Financial Risk What I Like About Math
What proportion of US adults have good jobs?
Good job = 30+ hours per week for anemployer who provides a regular pay-check.1
Do you have good job?
Yes, No, No, . . . , Yes, No, . . .
proportion =1 + 0 + 0 + ¨ ¨ ¨+ 1 + 0 + ¨ ¨ ¨
250,000,000an average
, but impractical
1Gallup Poll, www.gallup.com/poll/125639/gallup-good-jobs.aspx
Fred J. Hickernell, [email protected] • Average • 2/9/17 3/10
Average Travel Speed Average for a Large Population Financial Risk What I Like About Math
What proportion of US adults have good jobs?
Good job = 30+ hours per week for anemployer who provides a regular pay-check.1
Do you have good job?
Yes, No, No, . . . , Yes, No, . . .
proportion =1 + 0 + 0 + ¨ ¨ ¨+ 1 + 0 + ¨ ¨ ¨
250,000,000an average
, but impractical
1Gallup Poll, www.gallup.com/poll/125639/gallup-good-jobs.aspx
Fred J. Hickernell, [email protected] • Average • 2/9/17 3/10
Average Travel Speed Average for a Large Population Financial Risk What I Like About Math
What proportion of US adults have good jobs?
Good job = 30+ hours per week for anemployer who provides a regular pay-check.1
Do you have good job?
Yes, No, No, . . . , Yes, No, . . .
proportion =1 + 0 + 0 + ¨ ¨ ¨+ 1 + 0 + ¨ ¨ ¨
250,000,000an average, but impractical
1Gallup Poll, www.gallup.com/poll/125639/gallup-good-jobs.aspx
Fred J. Hickernell, [email protected] • Average • 2/9/17 3/10
Average Travel Speed Average for a Large Population Financial Risk What I Like About Math
What proportion of US adults have good jobs?
Good job = 30+ hours per week for anemployer who provides a regular pay-check.1
Do you have good job?
Yes, No, No, . . . , Yes, No, . . .
proportion =1 + 0 + 0 + ¨ ¨ ¨+ 1 + 0 + ¨ ¨ ¨
250,000,000an average, but impractical
=0 + 1 + ¨ ¨ ¨
30,000˘ 1% sample average ˘ sampling error
1Gallup Poll, www.gallup.com/poll/125639/gallup-good-jobs.aspx
Fred J. Hickernell, [email protected] • Average • 2/9/17 3/10
Average Travel Speed Average for a Large Population Financial Risk What I Like About Math
What proportion of US adults have good jobs?Good job = 30+ hours per week for anemployer who provides a regular pay-check.1
Do you have good job?
Yes, No, No, . . . , Yes, No, . . .
proportion =1 + 0 + 0 + ¨ ¨ ¨+ 1 + 0 + ¨ ¨ ¨
250,000,000an average, but impractical
=0 + 1 + ¨ ¨ ¨
30,000˘ 1% sample average ˘ sampling error
= 44.6%˘ 1% according to Gallup
The adults surveyed here are chosen randomly and independently of eachother.
The sampling error is « 1/a
sample size.
1Gallup Poll, www.gallup.com/poll/125639/gallup-good-jobs.aspx
Fred J. Hickernell, [email protected] • Average • 2/9/17 3/10
Average Travel Speed Average for a Large Population Financial Risk What I Like About Math
What proportion of US adults have good jobs?Good job = 30+ hours per week for anemployer who provides a regular pay-check.1
Do you have good job?
Yes, No, No, . . . , Yes, No, . . .
proportion =1 + 0 + 0 + ¨ ¨ ¨+ 1 + 0 + ¨ ¨ ¨
250,000,000an average, but impractical
=0 + 1 + ¨ ¨ ¨
30,000˘ 1% sample average ˘ sampling error
= 44.6%˘ 1% according to Gallup
The adults surveyed here are chosen randomly and independently of eachother. The sampling error is « 1/
a
sample size.
1Gallup Poll, www.gallup.com/poll/125639/gallup-good-jobs.aspx
Fred J. Hickernell, [email protected] • Average • 2/9/17 3/10
Average Travel Speed Average for a Large Population Financial Risk What I Like About Math
What proportion of US adults have good jobs?Good job = 30+ hours per week for anemployer who provides a regular pay-check.1
Do you have good job?
Yes, No, No, . . . , Yes, No, . . .
proportion =1 + 0 + 0 + ¨ ¨ ¨+ 1 + 0 + ¨ ¨ ¨
250,000,000an average, but impractical
=1 + 0 + ¨ ¨ ¨
1,000,000˘ ?? sample average ˘ sampling error
You pursue the big data web survey approach. The respondents are notindependent, but you hope that they have a small (0.05) correlation withjoblessness.
Big data does not eliminate the need for careful sampling.
1Gallup Poll, www.gallup.com/poll/125639/gallup-good-jobs.aspx
Fred J. Hickernell, [email protected] • Average • 2/9/17 3/10
Average Travel Speed Average for a Large Population Financial Risk What I Like About Math
What proportion of US adults have good jobs?Good job = 30+ hours per week for anemployer who provides a regular pay-check.1
Do you have good job?
Yes, No, No, . . . , Yes, No, . . .
proportion =1 + 0 + 0 + ¨ ¨ ¨+ 1 + 0 + ¨ ¨ ¨
250,000,000an average, but impractical
=1 + 0 + ¨ ¨ ¨
1,000,000˘ 79% sample average ˘ sampling error
You pursue the big data web survey approach. The respondents are notindependent, but you hope that they have a small (0.05) correlation withjoblessness. Big data does not eliminate the need for careful sampling.
1Gallup Poll, www.gallup.com/poll/125639/gallup-good-jobs.aspx
Fred J. Hickernell, [email protected] • Average • 2/9/17 3/10
Average Travel Speed Average for a Large Population Financial Risk What I Like About Math
What will happen to my investments?
Know portfolio value today and inthe past, but not the future
Questions about expected portfolio value, chance of losing 20% ofportfolio value, fair option prices, and more may be framed as:
average over ∞ number of scenarios =
ż
f (x)dx
which cannot be evaluated with pencil and paper ,
but you can get agood approximation taking the average of many scenarios .
I research how to do this efficiently .
Fred J. Hickernell, [email protected] • Average • 2/9/17 4/10
Average Travel Speed Average for a Large Population Financial Risk What I Like About Math
What will happen to my investments?
Know portfolio value today and inthe past, but not the future
Questions about expected portfolio value, chance of losing 20% ofportfolio value, fair option prices, and more may be framed as:
average over ∞ number of scenarios =
ż
f (x)dx
which cannot be evaluated with pencil and paper ,
but you can get agood approximation taking the average of many scenarios .
I research how to do this efficiently .
Fred J. Hickernell, [email protected] • Average • 2/9/17 4/10
Average Travel Speed Average for a Large Population Financial Risk What I Like About Math
What will happen to my investments?Know portfolio value today and inthe past, but not the future
Questions about expected portfolio value, chance of losing 20% ofportfolio value, fair option prices, and more may be framed as:
average over ∞ number of scenarios =
ż
f (x)dx
which cannot be evaluated with pencil and paper ,
but you can get agood approximation taking the average of many scenarios .
I research how to do this efficiently .
Fred J. Hickernell, [email protected] • Average • 2/9/17 4/10
Average Travel Speed Average for a Large Population Financial Risk What I Like About Math
What will happen to my investments?Know portfolio value today and inthe past, but not the future
Questions about expected portfolio value, chance of losing 20% ofportfolio value, fair option prices, and more may be framed as:
average over ∞ number of scenarios =
ż
f (x)dx
which cannot be evaluated with pencil and paper ,
but you can get agood approximation taking the average of many scenarios .
I research how to do this efficiently .
Fred J. Hickernell, [email protected] • Average • 2/9/17 4/10
Average Travel Speed Average for a Large Population Financial Risk What I Like About Math
What will happen to my investments?Know portfolio value today and inthe past, but not the future
Questions about expected portfolio value, chance of losing 20% ofportfolio value, fair option prices, and more may be framed as:
average over ∞ number of scenarios =
ż
f (x)dx
which cannot be evaluated with pencil and paper ,
but you can get agood approximation taking the average of many scenarios .
I research how to do this efficiently .
Fred J. Hickernell, [email protected] • Average • 2/9/17 4/10
Average Travel Speed Average for a Large Population Financial Risk What I Like About Math
What will happen to my investments?Know portfolio value today and inthe past, but not the future
Questions about expected portfolio value, chance of losing 20% ofportfolio value, fair option prices, and more may be framed as:
average over ∞ number of scenarios =
ż
f (x)dx
which cannot be evaluated with pencil and paper , but you can get agood approximation taking the average of many scenarios .
I research how to do this efficiently .
Fred J. Hickernell, [email protected] • Average • 2/9/17 4/10
Average Travel Speed Average for a Large Population Financial Risk What I Like About Math
What will happen to my investments?Know portfolio value today and inthe past, but not the future
Questions about expected portfolio value, chance of losing 20% ofportfolio value, fair option prices, and more may be framed as:
average over ∞ number of scenarios =
ż
f (x)dx
which cannot be evaluated with pencil and paper , but you can get agood approximation taking the average of many scenarios .I research how to do this efficiently .Fred J. Hickernell, [email protected] • Average • 2/9/17 4/10
Average Travel Speed Average for a Large Population Financial Risk What I Like About Math
August 12, 2016 News
Fred J. Hickernell, [email protected] • Average • 2/9/17 5/10
Average Travel Speed Average for a Large Population Financial Risk What I Like About Math
What I like about applied mathematics
Power to explain the non-intuitive: data do not speak for themselves
Ideas are recycledRigor + relevanceWe can learn it with each other’s help
Fred J. Hickernell, [email protected] • Average • 2/9/17 6/10
Average Travel Speed Average for a Large Population Financial Risk What I Like About Math
What I like about applied mathematics
Power to explain the non-intuitive: data do not speak for themselvesIdeas are recycled
Rigor + relevanceWe can learn it with each other’s help
Fred J. Hickernell, [email protected] • Average • 2/9/17 6/10
Average Travel Speed Average for a Large Population Financial Risk What I Like About Math
What I like about applied mathematics
Power to explain the non-intuitive: data do not speak for themselvesIdeas are recycledRigor + relevance
We can learn it with each other’s help
Fred J. Hickernell, [email protected] • Average • 2/9/17 6/10
Average Travel Speed Average for a Large Population Financial Risk What I Like About Math
What I like about applied mathematics
Power to explain the non-intuitive: data do not speak for themselvesIdeas are recycledRigor + relevanceWe can learn it with each other’s help
Fred J. Hickernell, [email protected] • Average • 2/9/17 6/10
Average Travel Speed Average for a Large Population Financial Risk What I Like About Math
Fred J. Hickernell, [email protected] • Average • 2/9/17 7/10
Slides available at www.slideshare.net/fjhickernell/iit-scholarship-weekend-average-talk-2017-february-9
Any questions?
Fred J. Hickernell, [email protected] • Average • 2/9/17 8/10
Thank you for coming!
Average Travel Speed Average for a Large Population Financial Risk What I Like About Math
Can you get a job with a mathematics degree?2
2Job rankings fromwww.careercast.com/jobs-rated/jobs-rated-report-2016-ranking-200-jobs
Fred J. Hickernell, [email protected] • Average • 2/9/17 9/10
Average Travel Speed Average for a Large Population Financial Risk What I Like About Math
How does university math differ from high school math?
Fewer contact hours with the instructor per course
Problems in quizzes and tests may not look so much like homework;you need to learn concepts
More responsibility to learn on your own
Opportunities for research with faculty
Fred J. Hickernell, [email protected] • Average • 2/9/17 10/10