1 / 61

Statistics Class 6

Statistics Class 6. February 8 th 2012. Reveiw. The number of incidents in which police were needed for a sample of 10 schools in Allegheny County is 7, 37, 3, 8, 48, 11, 6, 0, 10, 3. Using the range rule of thumb do you consider 48 incidents at one school unusual?. Measures of Variation.

lucus
Télécharger la présentation

Statistics Class 6

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Statistics Class 6 February 8th2012

  2. Reveiw The number of incidents in which police were needed for a sample of 10 schools in Allegheny County is 7, 37, 3, 8, 48, 11, 6, 0, 10, 3. Using the range rule of thumb do you consider 48 incidents at one school unusual?

  3. Measures of Variation Empirical Rule (68-95-99.7) for data with a Bell-Shaped Distribution. • About 68% of all values fall within 1 standard deviations of the mean. • About 95% of all values fall within 2 standard deviations of the mean. • About 99.7% of all values fall within 3 standard deviations of the mean.

  4. Measures of Variation Empirical Rule (68-95-99.7) for data with a Bell-Shaped Distribution.

  5. Measures of Variation Empirical Rule (68-95-99.7) for data with a Bell-Shaped Distribution.

  6. Measures of Variation IQ scores have a bell-shaped distribution with a mean of 100 and a standard deviation of 15. What percentage of IQ scores are between 70 and 130?

  7. Measures of Variation IQ scores have a bell-shaped distribution with a mean of 100 and a standard deviation of 15. What percentage of IQ scores are between 70 and 130?

  8. Coefficient of Variation • The Coefficient of Variation or CV for a set of nonnegative sample or population data, expressed as a percent, describes the standard deviation relative to the mean, and is given by the following: Sample Population

  9. Coefficient of Variation Compare the variation in the heights of men to the variation in weights of men, using these sample results obtained from Data Set 1 in Appendix B: for men, the heights yield a mean of 68.34 in. and standard deviation 3.02 in; the weights yield a mean of 172.55 lbs. and a standard deviation of 26.33 lbs.

  10. Coefficient of Variation Compare the variation in the heights of men to the variation in weights of men, using these sample results obtained from Data Set 1 in Appendix B: for men, the heights yield a mean of 68.34 in. and standard deviation 3.02 in; the weights yield a mean of 172.55 lbs. and a standard deviation of 26.33 lbs. heights: weights:

  11. Measures of Relative Standing A z score ( or standardized value) is the number of standard deviations that a given value x is above or below the mean. The z score is calculated by using one of the following: Sample Population

  12. Measures of Relative Standing We now consider a comparison of two individual data values as we try to determine which is more extreme: the 76.2in. Height of a man or the 237.1 lb weight of a man. Compare those two data values by finding their corresponding z scores. Use these sample results: Heights have mean in. and standard deviation in. Weights have mean lb and standard deviation lb.

  13. Measures of Relative Standing z scores, Unusual Values, and Outliers Ordinary values: . Unusual values: or . The data values that are unusual, i.e. have a z score less than -2 or greater than 2, are called outliers.

  14. Measures of Relative Standing A student scored 65 on a calculus test that had a mean of 50 and a standard deviation of 10: she scored a 30 on a history test with a mean of 25 and a standard deviation of 5. Compare her relative positions on the two tests.

  15. Measures of Relative Standing Percentiles Percentiles are measures of location, denoted , , …, which divide a set of data into 100 groups with about 1% of the values in each group. For example, the 50th percentile denoted has about 50% of the data values below and above it.

  16. Measures of Relative Standing Percentiles Finding the Percentile of a Data Value (Round result to the nearest whole number)

  17. Measures of Relative Standing Percentiles Finding the Percentile of a Data Value Consider this list of 35 sorted movies budgets taken from a simple random sample. Find the percentile for the value of $52 million.

  18. Measures of Relative Standing Percentiles Finding the Percentile of a Data Value Find the percentile for the value of $52 million.

  19. Measures of Relative Standing Percentiles Finding the Percentile of a Data Value Find the percentile for the value of $52 million.

  20. Measures of Relative Standing Percentiles Finding the Percentile of a Data Value Find the percentile for the value of $52 million.

  21. Measures of Relative Standing Percentiles Finding the Percentile of a Data Value Find the percentile for the value of $52 million.

  22. Measures of Relative Standing Percentiles Finding the Percentile of a Data Value Find the percentile for the value of $52 million. So the budget amount of $52 million is at the 37th percentile.

  23. Measures of Relative Standing Percentiles Converting a percentile to a Data Value To convert a percent to a data value we use the following formula where kth percentile.

  24. Measures of Relative Standing Percentiles Converting a percentile to a Data Value To convert a percent to a data value we use the following formula Tricky Part If L is not a whole number then round it up, then is the Lth value counting from the lowest. If L is a whole number, then is midway between the Lth value and the next value in the sorted set of data. So .

  25. Measures of Relative Standing Percentiles Converting a percentile to a Data Value Lets find the value of the Movie Budget that is at the 90th percentile.

  26. Measures of Relative Standing Percentiles Converting a percentile to a Data Value Lets find the value of the Movie Budget that is at the 90th percentile.

  27. Measures of Relative Standing Percentiles Converting a percentile to a Data Value Lets find the value of the Movie Budget that is at the 90th percentile.

  28. Measures of Relative Standing Percentiles Converting a percentile to a Data Value Lets find the value of the Movie Budget that is at the 90th percentile.

  29. Measures of Relative Standing Percentiles Converting a percentile to a Data Value Lets find the value of the Movie Budget that is at the 90th percentile.

  30. Measures of Relative Standing Percentiles Converting a percentile to a Data Value Lets find the value of the Movie Budget that is at the 90th percentile.

  31. Measures of Relative Standing Percentiles Converting a percentile to a Data Value Lets find the value of the Movie Budget that is at the 90th percentile.

  32. Measures of Relative Standing Percentiles Converting a percentile to a Data Value Lets find the value of the Movie Budget that is at the 90th percentile.

  33. Measures of Relative Standing Percentiles Converting a percentile to a Data Value Lets find the value of the Movie Budget that is at the 90th percentile.

  34. Measures of Relative Standing Percentiles Converting a percentile to a Data Value Lets find the value of the Movie Budget that is at the 90th percentile.

  35. Measures of Relative Standing Percentiles Converting a percentile to a Data Value Lets find the value of the Movie Budget that is at the 90th percentile. .

  36. Measures of Relative Standing Percentiles Converting a percentile to a Data Value Lets find the value of the Movie Budget that is at the 90th percentile. . L is not a whole number so we round up to the 32nd value.

  37. Measures of Relative Standing Percentiles Converting a percentile to a Data Value Lets find the value of the Movie Budget that is at the 90th percentile. We round up to the 32nd value. We count to the 32nd position in our chart.

  38. Measures of Relative Standing Percentiles Converting a percentile to a Data Value Lets find the value of the Movie Budget that is at the 90th percentile. We round up to the 32nd value. We count to the 32nd position in our chart.

  39. Measures of Relative Standing Percentiles Converting a percentile to a Data Value Lets find the value of the Movie Budget that is at the 90th percentile. We round up to the 32nd value. We count to the 32nd position in our chart. So the value of $150 million is at the 90th percentile, that is about 90% of the movies have budgets below $150 million.

  40. Measures of Relative Standing Percentiles Converting a percentile to a Data Value Now find the value of the Movie Budget that is at the 60th percentile.

  41. Measures of Relative Standing Percentiles Converting a percentile to a Data Value Now find the value of the Movie Budget that is at the 60th percentile.

  42. Measures of Relative Standing Percentiles Converting a percentile to a Data Value Now find the value of the Movie Budget that is at the 60th percentile. . L is a whole number so is midway between the 21st and 22nd positions on our chart

  43. Measures of Relative Standing Percentiles Converting a percentile to a Data Value Now find the value of the Movie Budget that is at the 60th percentile. . L is a whole number so is midway between the 21st and 22nd positions on our chart. So

  44. Measures of Relative Standing Percentiles Converting a percentile to a Data Value Now find the value of the Movie Budget that is at the 60th percentile. So So the value of $71 million is at the 60th Percentile.

  45. Measures of Relative Standing A teacher gives a 20-point test to 10 students. The scores are shown here. Find the percentile rank of a score of 12. 18, 15, 12, 6, 8, 2, 3, 5, 20, 10

  46. Measures of Relative Standing Using the same data as the previous slide find the value that corresponds to the 60th percentile.

  47. Measures of Relative Standing Quartiles Quartiles are measures of location, denoted , which divide a set of data into four groups with about 25% of the values in each group. • (First Quartile):Separates the bottom 25% of the sorted values from the top 75%. • (Second Quartile): Same as the median;separates the bottom 50% of the sorted values form the top 50% • (Third Quartile): Separates the bottom 75% of the sorted values from the top 25%. • Or use your calculator!

  48. Measures of Relative Standing Quartiles How to Find a Quartile Find the value of the first Quartile of the movie budget data. Hint: Finding is the same as find

  49. Measures of Relative Standing Quartiles How to Find a Quartile Find the value of the first Quartile of the movie budget data. Hint: Finding is the same as find So the rounding up we get 9. So the first Quartile of the movie budget data is $35 million

  50. Measures of Relative Standing 5-Number Summary and Boxplot For a set of data, the 5-number summary consists of the minimum value, the first quartile , the median (or second quartile ), the third Quartile , and the maximum value.

More Related