Statistics

Entering numeric data• On your iclicker.• You will be told when a numeric input is required• Press blue button to change mode.• Use the “up and down” arrow keys at the top to increase or decrease the

number. • Use the “left and right” arrow keys to move the cursor. • Press “send” when you have entered the desired answer.

Trial run• Starting now, enter a number in your head

between 0 and 99.• Press send when you are done.

Clicker question• Enter your height to the nearest inch.• For example if your height is 5’10” then enter

70 since

Clicker Q version 2• Enter which range your height falls in:• A) • B)• C) • D)• E)

What does the mean mean?• Numbers their mean value is

their sum divided by N,

What is the mean height of an American president?

• X: a president’s height. Its values are:• 64,66,66,67,67,67,68,68,68,68,68.5,69,69,69.5,70,70,70,70,70.5,

71,71,71,71,71.5,72,72,72,72,72,72,72,72,73,73,74,74,74,74,74.5,74.5,75,76

• N=42• Mean=(64+2x66+3x67+4x68+68.5+2x69+69.5+5x70+70.5+4x71

+71.5+8x72+2x73+4x74+2x74.5+75+76)/42=70.69

Height President Height President5ft4 James Madison 5ft11 George W. Bush

Grover ClevelandHerbert HooverWoodrow Wilson

5ft6 Benjamin HarrisonMartin Van Buren

5ft11.5 Richard Nixon

5ft7 John Quincy AdamsJohn AdamsWilliam McKinley

6ft James BuchananGerald R. FordJames GarfieldWarren HardingJohn F. KennedyJames MonroeWilliam H. TaftJohn Tyler

5ft8 Ulysses S. GrantWilliam H. HarrisonJames PolkZachary Taylor

6ft1 Andrew JacksonRonald Reagan

5ft8.5 Rutherford Hayes 6ft2 Chester ArthurGeorge BushFranklin D. RooseveltGeorge Washington

5ft9 Millard FillmoreHarry S. Truman

6ft2.5 Bill ClintonThomas Jefferson

5ft9.5 Jimmy Carter 6ft3 Lyndon B. Johnson

5ft10 Calvin CoolidgeAndrew JohnsonFranklin PierceTheodore Roosevelt

6ft4 Abraham Lincoln

5ft10.5 Dwight D. Eisenhower

What does the mean miss?Average height of a human, on average, has increased with time.Data collected over a long period of time can exhibit a trend.A process that is used to represent evolution of some random value over a

period of time is called a stochastic process.

Histogram of president heights

Histogram of midterm scores

Histogram of household incomes

President heights vs time

Other time-dependent statistics: sex ratio

2012 Olympian heights

The mean is not always representative of a typical value.

Household income in the United States

What does the median mean?• Given numbers x1 ,…, xN their MEDIAN is the number that is less than half

the numbers and greater than half the numbers.• If there is an even number of samples, the mean is usually the average of

the two middle values.• What is the median height for a U.S. president?

Clicker question: what is the median height of the first 42 us presidents?

A 68

B 73

C 71

D 76

Mean and median household incomes

• Compute the mean household income based on the data above

• Compute the median based on the data above.

Variance• The variance of numbers x1 ,…, xN is the sum of the

squares of their differences from their mean, divided by N-1.

• The sample deviation is the square root of the variance.

Which olympian are you most like?

Covariance• Covariance is a measure of how much two

variables vary together.

Body mass index

Formula for BMI

Clicker question• What is your BMI (round to the nearest whole

number). Enter as numerical input.

The case of Jackie Jeschelnig

• Height: 5'9" (175 cm) • Olympic Weight: 203 lbs (92 kg) • BMI=92/(1.75)^2 =30.04

BMI is correlated with body fat

Are tall people smarter?• How tall is Randy Newman?

why?

Other controversial correlations: height and intelligence and pay

• Height and intelligence• Why are tall people smarter?• Height and income• Height, income and intelligence• Best revenge is living long

Health statistics• The Centers for Disease Control web site has a

lot of data on various health statistics for the U.S.

• Example: Is obesity a problem in the U.S.?

Exercises• Compute the average height, average weight,

median height, median weight, variance of the heights, and variance of the weights from the following data taken from the following source

• Heights and weights data

Index Height X (Inches)

Weight Y(Pounds) BMI Z

1 65.78 112.99

2 71.52 136.49

3 69.40 153.03

4 68.22 142.34

5 67.79 144.30

6 68.70 123.30

7 69.80 141.49

8 70.01 136.46

9 67.90 112.37

10 66.78 120.67

Mean height: Height SD: Mean

weight: Weight SD: Mean BMI BMI SD

Names:__________ ___________ __________

Exercise 2• For each individual in the previous table,

compute the BMI of that individual.

Exercise 3• For each of the Olympic athletes in the following

table taken from fatchic compute the athlete’s BMI.

• What are the average heights and weights for the athletes?

• What is the variance in heights and weights of these athletes?

Name Sport Country Height Weight

Name Sport Country Height Weight

Khalil Mahmoud K Abir Abdelrahman Weightlifting Egypt 5 ft 4 in 165 lbs

Esmat Ahmed Weightlifting Egypt 5 ft 5 in 152 lbs

Marie-Eve Beauchemin-Nadeau Weightlifting Canada 5 ft 5 in 152 lbs

Maria Abakumova Javelin Throw Russian Federation 5 ft 10 in 187 lbs

Neide Barbosa Handball Angola 5 ft 10 in 172 lbs

Marthe Koala Women's 100 M Hurdles Burkina Faso 5 ft 9 in 150 lbs

Amanda Bingson Women's Hammer Throw USA 5 ft 5 in 201 lbs

Jillian Camarena-Williams Women's Shot Put USA 5 ft 10 in 249 lbs

Nina Kamto Njitam Handball France 5 ft 10 in 163 lbs

Delphine Reau Shooting France 5 ft 7 in 159 lbs