Statistics

What does the mean mean?

• Numbers x1 ,…, xN their mean value is their sum divided by N

What is the mean height of an American president?

• X values are:• 64,66,66,67,67,67,68,68,68,68,68.5,69,6

9,69.5,70,70,70,70,70.5,71,71,71,71,71.5,72,72,72,72,72,72,72,72,73,73,74,74,74,74,74.5,74.5,75,76

• N=42• Mean=(64+2x66+3x67+4x68+68.5+2x

69+69.5+5x70+70.5+4x71+71.5+8x72+2x73+4x74+2x74.5+75+76)/42=70.69

Histogram of president heights

Obama is 6'1 (73 inches)

and tied with Andrew

Jackson and Ronald

Reagan for 9th tallest president.

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.

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

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.

Are tall people smarter?

• How tall is Randy Newman?

why?

Statistical significance

• The significance level of a test is a traditional frequentist statistical hypothesis testing concept. In simple cases, it is defined as the probability of making a decision to reject the null hypothesis when the null hypothesis is actually true (a decision known as a Type I error, or "false positive determination"). The decision is often made using the p-value: if the p-value is less than the significance level, then the null hypothesis is rejected. The smaller the p-value, the more significant the result is said to be.

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.

Body mass index

Human metabolism

• During respiration, plants and animals consume oxygen and emit carbon dioxide. Such is life! Just for breathing, humans emit per person each day some 1,140 grams of CO2, assuming they eat normally and follow the mean diet of 2,800 kcal (more or less, since the caloric efficiency of burnt carbon also depends on the type of food: fat, protein or carbohydrates).

• The amount of CO2 emitted per person per day is not negligible. It is equivalent to the emission of a car in a 5 km stretch.

• If we multiply the 1,140 grams/day by 6 billion persons then, just for breathing, humanity emits per year some 2.5 billion tons of CO2 . . . a considerable amount, more than the reduction required by the Kyoto Protocol (that reduction is a bit less than 1 billion tons, 5% of the 1990 emission).

• But the net balance between the carbon absorbed by feeding and the carbon emitted by breathing is almost zero, so is the same how many people we are. Nevertheless a little bit of the carbon we eat is transformed in methane, wich molecule has a greater potential of warming than the CO2 ...

• Basal metabolic rate

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.?