Statistics

1. Statistics

2. 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.

3. Trial run • Starting now, enter a number in your head between 0 and 99. • Press send when you are done.

4. Clicker question • Enter your height to the nearest inch. • For example if your height is 5’10” then enter 70 since

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

6. What does the mean mean? • Numbers their mean value is their sum divided by N,

7. 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

9. 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.

10. Histogram of president heights

11. President heights vs time

12. Other time-dependent statistics: sex ratio

13. 2012 Olympian heights

14. The mean is not always representative of a typical value.

15. 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?

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

17. Household income in the United States

18. Mean and median household incomes • Compute the mean household income based on the data above • Compute the median based on the data above.

19. Variance • The variance of numbers x1 ,…, xNis 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.

21. Which olympian are you most like?

22. Covariance • Covariance is a measure of how much two variables vary together.

24. Body mass index

25. Formula for BMI

26. Clicker question • What is your BMI (round to the nearest whole number). Enter as numerical input.

27. The case of Jackie Jeschelnig

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

29. BMI is correlated with body fat

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

31. why?

32. 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

33. 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.?

34. 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

35. Names:__________ ___________ __________

36. Exercise 2 • For each individual in the previous table, compute the BMI of that individual.

37. 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?