Statistics. What does the mean mean? Numbers x 1,…, x N their mean value is their sum divided by N.

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Presentation transcript:

Statistics

What does the mean mean? Numbers x 1,…, x N their mean value is their sum divided by N

What is the mean height of an American presidentWhat is the mean height of an American president? X: a president’s height. Its values are: 64,66,66,67,67,67,68,68,68,68,68.5,69,69,69.5,7 0,70,70,70,70.5,71,71,71,71,71.5,72,72,72,72,72,72,72,72,73,73,74,74,74,74,74.5,74.5,75,76 N=42 Mean =(64+2x66+3x67+4x x x x x72+2x73+4x74+2 x )/42= 70.69

HeightPresidentHeightPresident 5ft4James Madison5ft11George W. Bush Grover Cleveland Herbert Hoover Woodrow Wilson 5ft6Benjamin Harrison Martin Van Buren 5ft11.5Richard Nixon 5ft7John Quincy Adams John Adams William McKinley 6ftJames Buchanan Gerald R. Ford James Garfield Warren Harding John F. Kennedy James Monroe William H. Taft John Tyler 5ft8Ulysses S. Grant William H. Harrison James Polk Zachary Taylor 6ft1Andrew Jackson Ronald Reagan 5ft8.5Rutherford Hayes6ft2Chester Arthur George Bush Franklin D. Roosevelt George Washington 5ft9Millard Fillmore Harry S. Truman 6ft2.5Bill Clinton Thomas Jefferson 5ft9.5Jimmy Carter6ft3Lyndon B. Johnson 5ft10Calvin Coolidge Andrew Johnson Franklin Pierce Theodore Roosevelt 6ft4Abraham Lincoln 5ft10.5Dwight D. Eisenhower

Obama is 6'1 (73 inches) and tied with Andrew Jackson and Ronald Reagan for 9th tallest president.

What does the mean miss? Two random variables are correlated if an increase in one corresponds to an increase in the other. For example, tall people, on average, weigh more. Average height of a human, on average, has increased with time.

President heights vs time

Histogram of president heights

Other time-dependent statistics: sex ratio

What does the median mean? Given numbers x 1,…, x N 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 42 us presidents? A68 B73 C71 D76

Household income in the United States

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 x 1,…, x N 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 BMI=Mass (kg)/(Height(m))^2 =(weight(lb)/(height (in)^2)*703

The case of Jackie Jeschelnig

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

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.?