1. Last lecture summary Which measures of central tendency do you know? Which measures of variability do you know? Empirical rule Population, census, sample, statistic, parameter Statistical inference 68% 95% 99.7%

2. Statistical jargon population (census) vs. sample parameter (population) vs. statistic (sample)

3. Sampling Representative sample, random sample Sampling with/without replacement Bias

4. New stuff

5. Bessel’s correction www.udacity.com – Statistics

6. Sample vs. population SD

7. Median absolute deviation (MAD) standard deviation is not robust IQR is robust mean absolute deviation MAD – a robust equivalent of the standard deviation Take your data, find median, calculate absolute deviation from the median, find the median of absolutes deviations

8. Median absolute deviation (MAD) DataMedian deviationAbsolute deviation 5 10 30 20 30 5 15 10 15 Median: MAD:

9. NORMAL DISTRIBUTION

10. Playing chess Pretend I am a chess player. Which of the following tells you most about how good I am: 1. My rating is 1800. 2. 8110 th place among world competitive chess players. 3. Ranked higher than 88% of competitive chess players.

11. Distribution Distribution of scores in one particular year We should use relative frequencies and convert all absolute frequencies to proportions.

12. Height data – absolute frequencies http://wiki.stat.ucla.edu/socr/index.php/SOCR_Data_Dinov_020108_HeightsWeights

13. Height data – relative frequencies

15. 30% What proportion of values is between 170 cm and 173.75 cm? 173.5

16. Height data – relative frequencies What proportion of values is between 170 cm and 175 cm? We can’t tell for certain.

17. How should we modify data/histogram to allow us a more detail? 1. Adding more value to the dataset 2. Increasing the bin size 3. A smaller bin size

18. Height data – relative frequencies What proportion of values is between 170 cm and 175 cm? 36%

19. Height data – relative frequencies

21. Normal distribution recall the empirical rule 68-95-99.7

22. STANDARD NORMAL DISTRIBUTION

23. Who is more popular?

24. Who is more popular s.d. = 36 s.d. = 60 Z = -3.53 Z = -2.57

25. Standardizing

26. Formula

27. Quiz What does a negative Z-score mean? 1. The original value is negative. 2. The original value is less than mean. 3. The original value is less than 0. 4. The original value minus the mean is negative.

28. Quiz II If we standardize a distribution by converting every value to a Z-score, what will be the new mean of this standardized distribution? If we standardize a distribution by converting every value to a Z-score, what will be the new standard deviation of this standardized distribution?

29. Standard normal distribution

30. Z Z – number of standard deviations away from the mean If the Z-value is +1, how many percent are less than that value? cca 84 % 0 +1+2+3-2 -3

31. Proportion of human heights

32. +1-2+20

33. Quiz Approximately what proportion of people is smaller than 168 cm? 173178 183 168163 16%

34. Quiz Approximately what proportion of people is higher than 183 cm? 173178 183 168163 2.5%

35. Quiz Approximately what proportion of people is between 163 cm and 178 cm high? 173178 183 168163 81.5%

36. Quiz Approximately what proportion of people is smaller than 180 cm? 173178 183 168163 ca 91.5%

37. Quiz What is the probability of randomly selecting a height in the sample that is >5 standard deviations above the mean? 1. 0.01 2. 0.3 3. 0.8 4. 0.99

38. Quiz What is the probability of randomly selecting a height in the sample that is <5 standard deviations below the mean? 1. 0.01 2. 0.3 3. 0.8 4. 0.99

39. Quiz What proportion of the data is either below 2 standard deviations or above 2 standard deviations from the mean for a normal distribution? 95% 2.5%

40. Z-table What is the proportion less than the point with the Z-score -2,75?