Frequency distribution

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Frequency distribution

  1. 1. Frequency Distribution
  2. 2. Frequency Distribution—  A representation, in a tabular format, which displays the number of observations within a given interval. The intervals must be mutually exclusive (each score must belong to exactly one class) and exhaustive (Including every possible element).
  3. 3. Question— Howdo we construct a frequency distribution table?
  4. 4. Let’s Try!!!— Agesof 50 men randomly selected from a population who died in gunfire are given. Construct a frequency distribution table having 7 classes.
  5. 5. 19 18 30 40 41 33 73 2523 25 21 33 65 17 20 7647 69 20 31 18 24 35 2417 36 65 70 22 25 65 1624 29 42 37 26 46 27 6321 27 23 25 71 37 75 2527 23
  6. 6. Determine the range.R = Highest Value – Lowest Value R = 76 – 16 = 60
  7. 7. —  Find the class width (c). Range R class width = ⇔ c= number of classes k 60 c = = 8.57 = 9 7
  8. 8. Write the classes starting with lowest score. Classes Tally Marks Freq. 70 – 78 61 – 69 52 – 60 43 – 51 34 – 42 25 – 33 16 – 24
  9. 9. Classes Class Tally Marks Freq. x boundaries 70 – 78 69.5 – 78.5 ///// 5 74 61 – 69 60.5 – 69.5 ///// 5 65 52 – 60 51.5 – 60.5 0 56 43 – 51 42.5 – 51.5 // 2 47 34 – 42 33.5 – 42.5 /////-// 7 38 25 – 33 24.5 – 33.5 /////-/////-//// 14 29 16 – 24 15.5 – 24.5 /////-/////-/////-// 17 20
  10. 10. General Process of Constructing a Frequency Table— STEP 1: Determine the range. Range (R)= Highest Value – Lowest ValueExample in data: 29,55,65,23,45,86,44 Find Range
  11. 11. —  STEP 2. Determine the tentative number of classes (k)—  Note:—  These classes are usually specified in question.—  The number of classes should be between 5 and 20. The actual number of classes may be affected by convenience or other subjective factors.
  12. 12. — STEP 3. Find the class width by dividing the range by the number of classes. Rangeclass width or class mark = number of classes R⇔ c= k (Always round – off )
  13. 13. — STEP 4. Determine the frequency for each class by referring to the tally columns and present the results in a table.
  14. 14. When constructing frequencytables, the following guidelinesshould be followed.—  The classes must be mutually exclusive. That is, each score must belong to exactly one class.—  Include all classes, even if the frequency might be zero.
  15. 15. — Allclasses should have the same width, although it is sometimes impossible to avoid open – ended intervals such as “65 years or older”.— The number of classes should be between 5 and 20.
  16. 16. Using Table:— What is the lower class limit of the highest class? Upper class limit of the lowest class?— Find the class mark of the class 43 – 51.— What is the frequency of the class 16 – 24?
  17. 17. SLOPE
  18. 18. SLOPESlope is a measure of steepness
  19. 19. Types of Slope Zero NegativePositive Undefined or No Slope
  20. 20. If given 2 points ona line, you may findthe slope using theformula m = y2 – y1 x2 – x1
  21. 21. Find the slope of the line through the points (3,7) and (5, 19). x1 y1 x2 y2m = 19 – 7 m = 12 m=6 5–3 2
  22. 22. Find the slope(3, 4) and (-6, -2)
  23. 23. If given an equation of a line, there are 2 ways to find theslope and y-intercept.
  24. 24. One method is towrite the equation inslope-intercept form,which is y = mx + b. slope y-intercept
  25. 25. Find the slope and y-intercept of thefollowing equations. y = 3x + ½ slope= 3 y-intercept = ½
  26. 26. 3x + 5y = 10First, solve the equation for y. 3x + 5y = 10 5y = -3x + 10 y = -3/5 x + 2 m= -3/5 b=2
  27. 27. Another method to find the slope if given an equation of a line is to write the equationin the form Ax + By = C.m = -A/B, b = C/B
  28. 28. Find the slope and y-intercept of thefollowing equations. A B C 8x + 11y = 7m= -8/11 b = 7/11
  29. 29. -6x = 2y + 14First, rewrite the equation in the form Ax + By = C. -6x - 2y = 14m= 6/-2 b = 14/-2m= -3 b = -7
  30. 30. If given the graph of a line, find the slope by using the “triangle” method tofind the rise over run.
  31. 31. rise = 4 m= rise runrun = 5 m= 4/5
  32. 32. Feedback form MET’s Institute of Management, Bhujbal Knowledge City, Adgaon, Nashik  1. Name of the student:2 . Graduation in:3. Please tick whether you had learnt statistics in your graduation level: Yes No4. Please grade yourself according to you in which categoryyou lie in the knowledge of mathematics and statistics1.Poor 2. Not good 3.Average 4.Good 5.Excellent
  33. 33. 5. Whether Induction on basics of Mathematics and Statistics was fruitful for you ? Yes / No If Yes then please state why?6.  Do you need any change in the current teaching methodology adopted for statistics? 7. Any suggestions related to the subjectstatistics:
  34. 34. TheEnd

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