Содержание
- 2. Frequency Distributions and Their Graphs Section 2.1
- 3. Frequency Distributions 102 124 108 86 103 82 71 104 112 118 87 95 103 116
- 4. Frequency Distributions Classes - the intervals used in the distribution Class width - the range divided
- 5. Frequency Distributions Midpoint - the sum of the limits divided by 2 lower class limit +
- 6. 78 90 102 114 126 3 5 8 9 5 67 79 91 103 115 Do
- 7. 67 - 78 79 - 90 91 - 102 103 - 114 115 - 126 3
- 8. Frequency Histogram A bar graph that represents the frequency distribution of the data set horizontal scale
- 9. 1 2 6 . 5 1 1 4 . 5 1 0 2 . 5 9
- 10. Relative Frequency Histogram A bar graph that represents the relative frequency distribution of the data set
- 11. Relative Frequency Histogram Time on Phone minutes Relative frequency on vertical scale Relative frequency
- 12. Frequency Polygon A line graph that emphasizes the continuous change in frequencies horizontal scale uses class
- 13. Frequency Polygon 9 8 7 6 5 4 3 2 1 0 5 9 8 5
- 14. Ogive Also called a cumulative frequency graph A line graph that displays the cumulative frequency of
- 15. Ogive An ogive reports the number of values in the data set that are less than
- 16. More Graphs and Displays Section 2.2
- 17. Stem-and-Leaf Plot 102 124 108 86 103 82 71 104 112 118 87 95 103 116
- 18. Stem-and-Leaf Plot 6 | 7 | 8 | 9 | 10 | 11 | 12 |
- 19. 6 | 7 7 | 1 8 8 | 2 5 6 7 7 9 |
- 20. Stem-and-Leaf with two lines per stem 6 | 7 7 | 1 7 | 8 8
- 21. Dot Plot 66 76 86 96 106 116 126 -contains all original data -easy way to
- 22. NASA budget (billions of $) divided among 3 categories. Pie Chart / Circle Graph Used to
- 23. Total Pie Chart Billions of $ Human Space Flight 5.7 Technology 5.9 Mission Support 2.7 14.3
- 24. Pareto Chart -A vertical bar graph in which the height of the bar represents frequency or
- 25. Scatter Plot Absences Grade Absences (x) x 8 2 5 12 15 9 6 y 78
- 26. Time Series Chart / Line Graph - Quantitative entries taken at regular intervals over a period
- 27. Measures of Central Tendency Section 2.3
- 28. Measures of Central Tendency Mean: The sum of all data values divided by the number of
- 29. 2 4 2 0 40 2 4 3 6 Calculate the mean, the median, and the
- 30. 0 2 2 2 3 4 4 6 40 2 4 2 0 40 2 4
- 31. Mode: The mode is 2 since it occurs the most times. Calculate the mean, the median,
- 32. Median: Sort data in order. Mode: The mode is 2 since it occurs the most times.
- 33. Uniform Symmetric Skewed right positive Skewed left negative Mean = Median Mean > Median Mean Shapes
- 34. A weighted mean is the mean of a data set whose entries have varying weights X
- 35. Weighted Mean A student receives the following grades, A worth 4 points, B worth 3 points,
- 36. The mean of a frequency distribution for a sample is approximated by X = where x
- 37. Mean of Grouped Data The heights of 16 students in a physical ed. class: Height Frequency
- 38. Measures of Variation Section 2.4
- 39. Closing prices for two stocks were recorded on ten successive Fridays. Calculate the mean, median and
- 40. Closing prices for two stocks were recorded on ten successive Fridays. Calculate the mean, median and
- 41. Range for A = 67 – 56 = $11 Range = Maximum value – Minimum value
- 42. The deviation for each value x is the difference between the value of x and the
- 43. – 5.5 – 5.5 – 4.5 – 3.5 – 0.5 1.5 1.5 5.5 5.5 5.5 56
- 44. Population Variance Sum of squares – 5.5 – 5.5 – 4.5 – 3.5 – 0.5 1.5
- 45. Population Standard Deviation Population Standard Deviation: The square root of the population variance. The population standard
- 46. Sample Variance and Standard Deviation To calculate a sample variance divide the sum of squares by
- 47. Interpreting Standard Deviation Standard deviation is a measure of the typical amount an entry deviates (is
- 48. Summary Range = Maximum value – Minimum value
- 49. Data with symmetric bell-shaped distribution have the following characteristics. About 68% of the data lies within
- 50. The mean value of homes on a certain street is $125,000 with a standard deviation of
- 51. The mean value of homes on a certain street is $125,000 with a standard deviation of
- 52. Chebychev’s Theorem For k = 3, at least 1 – 1/9 = 8/9 = 88.9% of
- 53. Chebychev’s Theorem The mean time in a women’s 400-meter dash is 52.4 seconds with a standard
- 54. Chebychev’s Theorem The mean time in a women’s 400-meter dash is 52.4 seconds with a standard
- 55. Standard Deviation of Grouped Data Sample standard deviation = See example on pg 82 f is
- 56. Estimates with Classes When a frequency distribution has classes, you can estimate the sample mean and
- 57. Measures of Position Section 2.5
- 58. Fractiles – numbers that divide an ordered data set into equal parts. Quartiles (Q1, Q2 and
- 59. You are managing a store. The average sale for each of 27 randomly selected days in
- 60. The data in ranked order (n = 27) are: 17 19 20 23 27 28 30
- 61. Interquartile Range – the difference between the third and first quartiles IQR = Q3 – Q1
- 62. Box and Whisker Plot 55 45 35 25 15 A box and whisker plot uses 5
- 63. Percentiles Percentiles divide the data into 100 parts. There are 99 percentiles: P1, P2, P3…P99. A
- 64. Percentiles 114.5 falls on or above 25 of the 30 values. 25/30 = 83.33. So you
- 65. Standard Scores Standard score or z-score - represents the number of standard deviations that a data
- 66. Standard Scores The test scores for a civil service exam have a mean of 152 and
- 67. (c) (a) (b) A value of x = 161 is 1.29 standard deviations above the mean.
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