Statistics

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Statistics

  1. 1. CHAPTER 6 S TAT I S T I C S
  2. 2.  is the science of the collection, organization, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments.
  3. 3. STATISTICS Class intervals a set of numerical data that is grouped into several classes and the range of each class is known as class interval
  4. 4.  There should be between 5 and 20 classes. The class width should be an odd number. This will guarantee that the class midpoints are integers instead of decimals. The classes must be mutually exclusive. This means that no data value can fall into two different classes
  5. 5.  The classes must be all inclusive. This means that all data values must be included. The classes must be continuous. There are no gaps in a frequency distribution. Classes that have no values in them must be included (unless its the first or last class which are dropped). The classes must be equal in width.
  6. 6. Class intervals Find the largest and smallest values Compute the Range = Maximum - Minimum Select the number of classes desired. This is usually between 5 and 20. Find the class width by dividing the range by the number of classes and rounding up. Pick a suitable starting point less than or equal to the minimum value.
  7. 7. STATISTICSThe data below shows the marks obtained by 40 studentsin a monthly test. 99 88 75 92 58 75 80 70 64 42 70 58 90 68 50 78 43 89 45 93 61 81 58 65 69 76 88 58 91 67 71 52 55 40 80 80 78 46 61 69
  8. 8. STATISTICSThe lowest value : 40The highest value : 99Difference : 99-40 = 59Width of class : 5 5959 5Number of class intervals = 5 12
  9. 9. The lowest value : 40The highest value : 99Difference : 99-40 = 59Width of class : 10Number of class intervals = 59 10 6
  10. 10. Class Limit- Lower limit : the lowest value of the class interval- Upper limit: the highest value of the class interval
  11. 11. Class Limit
  12. 12. Class Boundary-lower boundary is the midpoint between the lower limit of the class interval and the upper limit of the previous class interval- Upper boundary is the midpoint between the upper limit of the class interval and the lower limit of the succeeding class interval
  13. 13. Class boundary40 - 49 50 – 59 60 – 69 Lower Upper boundary boundary 1 1 (49 50) (59 60) 2 2 49.5 59.5
  14. 14. Class Boundary
  15. 15. HISTOGRAM bar chart with i. horizontal axis represented by the upper boundary and the vertical axis represented by the frequencyOr ii. frequency versus midpoint
  16. 16. Histogram Histogram of marks 10 9 8 7 6frequency 5 4 3 2 1 0 29.5-39.5 39.5-49.5 49.5-59.5 59.5-69.5 69.5-79.5 79.5-89.5 89.5-99.5 Upper boundary(marks)
  17. 17. HISTOGRAM 10 Histogram of Marks 9 8 7Frequency 6 5 4 3 2 1 0 44.5 54.5 64.5 .74.5 84.5 94.5 midpoints ( marks )
  18. 18. Frequency polygon is a closed line graph Two methods : i. From histogram ii. frequency versus midpoint
  19. 19. Histogram and Frequency polygon 10 9 8 7 6Frequency 5 4 3 2 1 0 29.5-39.5 39.5-49.5 49.5-59.5 59.5-69.5 69.5-79.5 79.5-89.5 89.5-99.5 99.5-109.5 Upper boundary (marks )
  20. 20. Frequency polygon Frequency polygon of marks 10 9 8 7Frequency 6 5 4 3 2 1 0 34.5 44.5 54.5 64.5 .74.5 84.5 94.5 104.5 Midpoint (marks)
  21. 21. Cumulative Frequency Table Must add a class interval with 0 frequency
  22. 22.  Ogive : Cumulative frequency curve Cumulative frequency versus upper boundaries
  23. 23. Ogive of marks 45 40 35Cumulative frequency 30 25 20 15 10 5 0 29.5 39.5 49.5 59.5 69.5 79.5 89.5 99.5 Upper boundary ( marks )
  24. 24. Measures of Dispersion - the amount or distances the values are spread out in a set of data i. Range :midpoint of the highest class – midpoint of the lowest class ii. Median : the value at half of the distribution iii. First quartile(Q1): the value at the first quarter iv. Third quartile (Q3): the value at the third quarter v. Interquartile range : Q3 – Q1
  25. 25. Ogive of marks 45 40 35Cumulative frequency 30 25 20 15 10 5 0 29.5 39.5 49.5 59.5 69.5 79.5 89.5 99.5 Upper boundary ( marks )
  26. 26. Exercise 1: SPM JUN’09
  27. 27. a) Complete the table belowMarks Frequency Midpoint Upper boundary Cumulative frequency60-64 0 62 64.5 065-69 2 67 69.5 270-74 6

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