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Chapter 2

Chapter 2. Frequency Distributions and Graphs. Outline. Introduction Organizing Data Histograms, Frequency Polygons, and Ogives Other Types of Graphs(pie or circular graph). Objectives. Organize data using frequency distributions.

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Chapter 2

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  1. Chapter 2 Frequency Distributions and Graphs

  2. Outline Introduction Organizing Data Histograms, Frequency Polygons, and Ogives Other Types of Graphs(pie or circular graph)

  3. Objectives Organize data using frequency distributions. Represent data in frequency distributions graphically using histograms, frequency, polygons, and ogives.

  4. Organizing Data • When data are collected in original form, they are calledraw data. • When the raw data is organized into afrequency distribution, the frequency will be the number of values in a specific class of the distribution. • A frequency distribution is the organizing of raw data in table form, using classes and frequencies.

  5. Types of frequency distribution 1. Ungroup frequency distribution. • Frequency distribution is called ungroup frequency distribution if the RANGE of data is not large. Example:-Number of girls in a 4-child family etc. 2. Group frequency distribution. • Frequency distribution is called group frequency distribution if the RANGE of data is large.

  6. daily people smoking cigarettes .50 peoples surveyed the following points come out.

  7. Frequency distribution

  8. Histogram,

  9. Histogram

  10. Frequency polygon

  11. Pie chart

  12. Cumulative frequency

  13. Grouped Frequency Distributions • Grouped frequency distributions(continuose) -can be used when the range of values in the data set is very large. The data must be grouped into classes that are more than one unit in width. • Examples - the life of boat batteries in hours.

  14. Categorical frequency distributions- can be used for data that can be placed in specific categories • Examples - political affiliation, religious affiliation,blood type , nationality of student in the university, colors of eyes, etc.

  15. Blood group are given in table. make a frequency distribution .

  16. Blood Type Frequency Distribution -

  17. Histogram

  18. Frequency polygon

  19. Pie graph

  20. Frequency Distributions 102 124 108 86 103 82 71 104 112 118 87 95 103 116 85 122 87 100 105 97 107 67 78 125 109 99 105 99 101 92 Make a frequency distribution table with five classes. Minimum value= Maximum value = Key values:

  21. Steps to Construct aFrequency Distribution 1. Choose the number of classes 2. Calculate the Class Width Find the range = maximum value – minimum. Then divide this by the number of classes. Finally, round up to a convenient number. (125 - 67) / 5 = 11.6 Round up to 12. 3. Determine Class Limits The lower class limit is the lowest data value that belongs in a class and the upper class limit is the highest. Use the minimum value as the lower class limit in the first class. (67) 4. Mark a tally | in appropriate class for each data value. After all data values are tallied, count the tallies in each class for the class frequencies.

  22. Construct a Frequency Distribution Minimum = 67, Maximum = 125 Number of classes = 5 Class width = 12 3 5 8 9 5 Class Limits Tally 78 90 102 114 126 67 79 91 103 115 Do all lower class limits first.

  23. Frequency Histogram Boundaries 66.5 - 78.5 78.5 - 90.5 90.5 - 102.5 102.5 -114.5 114.5 -126.5 3 5 8 9 5 Class 67 - 78 79 - 90 91 - 102 103 -114 115 -126 Time on Phone 9 9 8 8 7 6 5 5 5 4 3 3 2 1 0 7 8 . 5 9 0 . 5 1 0 2 . 5 1 1 4 . 5 1 2 6 . 5 6 6 . 5 minutes

  24. Frequency Histogram Boundaries 66.5 - 78.5 78.5 - 90.5 90.5 - 102.5 102.5 -114.5 114.5 -126.5 3 5 8 9 5 Class 67 - 78 79 - 90 91 - 102 103 -114 115 -126 Time on Phone 9 9 8 8 7 6 5 5 5 4 3 3 2 1 0 7 8 . 5 9 0 . 5 1 0 2 . 5 1 1 4 . 5 1 2 6 . 5 6 6 . 5 minutes

  25. Other Information Midpoint:(lower limit + upper limit) / 2 Relative frequency:class frequency/total frequency Cumulative frequency:Number of values in that class +in lower class Cumulative Frequency Midpoint Relative Frequency Class (67 + 78)/2 3/30 67 - 78 79 - 90 91 - 102 103 - 114 115 - 126 72.5 84.5 96.5 108.5 120.5 0.10 0.17 0.27 0.30 0.17 3 8 16 25 30 3 5 8 9 5

  26. Relative Frequency Histogram Time on Phone Relative frequency minutes Relative frequency on vertical scale

  27. 30 30 25 20 16 10 8 3 0 0 66.5 78.5 90.5 102.5 114.5 126.5 Ogive An ogive reports the number of values in the data set that are less than or equal to the given value, x. Minutes on Phone Cumulative Frequency minutes

  28. EXAMPLE – Creating a Frequency Distribution Table Mr. Bill of Auto USA wants to develop tables, charts, and graphs to show the typical selling price on various dealer lots. The table on the reports only the price of the 80 vehicles sold last month at WhitnerAutoplex.

  29. Constructing a Frequency Table - Example Step 1: Decide on the number of classes. Numbers of classes = 7 Step 2:Determine the class interval or width. The formula is: i (H-L)/kwhere I is the class interval, H is the highest observed value, L is the lowest observed value, and k is the number of classes. ($35,925 - $15,546)/7 = $2,911=3000 Round up to some convenient number .

  30. Constructing a Frequency Table – Example: Step 3: Set the individual class limits

  31. Constructing a Frequency Table Step 4: Tally the vehicle selling prices into the classes. Step 5: Count the number of items in each class.

  32. To convert a frequency distribution to a relative frequency distribution, each of the class frequencies is divided by the total number of observations.

  33. Graphic Presentation of a Frequency Distribution The three commonly used graphic forms are: • Histograms • Frequency polygons • Cumulative frequency distributions

  34. Histogram • Histogram for a frequency distribution based on quantitative data is very similar to the bar chart showing the distribution of qualitative data. The classes are marked on the horizontal axis and the class frequencies on the vertical axis. The class frequencies are represented by the heights of the bars.

  35. Frequency Polygon • A frequency polygon also shows the shape of a distribution and is similar to a histogram. • It consists of line segments connecting the points formed by the intersections of the class midpoints and the class frequencies.

  36. Cumulative Frequency Distribution

  37. Numbers of mile travel by instructor from home to campus

  38. Number of Miles Traveled -

  39. An accident occurred in 2011. 40 people were injured. make a frequency distribution and show which class people injured more using numbers of classes 3. following are the ages of different classes.

  40. Class Class Frequency Cumulative limits Boundaries frequency 24 - 37 23.5 - 37.5 9 4 38 - 51 37.5 - 51.5 11 20 52 - 65 51.5 - 65.5 20 40

  41. Terms Associated with a Grouped Frequency Distribution • Theclass widthfor a class in a frequency distribution is found by subtracting the lower (or upper) class limit of one class minus the lower (or upper) class limit of the previous class.

  42. Constructing a Frequency Distribution • There should be between 5 and 20 classes. • The class width should be an odd number. • The classes must be mutually exclusive.

  43. Guidelines for Constructing a Frequency Distribution • The classes must be continuous. • The classes must be exhaustive. • The class must be equal in width.

  44. Important points for frequency distribution Find the highest and lowest value. • Find the range. • Select the number of classes desired. • Find the width by dividing the range by the number of classes and rounding up.

  45. Procedure for Constructing a Grouped Frequency Distribution • Select a starting point (usually the lowest value); add the width to get the lower limits. • Find the upper class limits. • Find the boundaries. • Tally the data, find the frequencies, and find the cumulative frequency.

  46. Grouped Frequency Distribution - Example • In a survey of 20 patients who smoked, the following data were obtained. Each value represents the number of cigarettes the patient smoked per day. Construct a frequency distribution using six classes. (The data is given on the next slide.)

  47. Construct frequency distributions using numbers of classes 6.

  48. Grouped Frequency Distribution - Example • Step 1:Find the highest and lowest values: H = 22 and L = 5. • Step 2:Find the range: R = H– L = 22 – 5 = 17. • Step 3:Select the number of classes desired. In this case it is equal to 6.

  49. Grouped Frequency Distribution - Example • Step 4:Find the class width by dividing the range by the number of classes. Width = 17/6 = 2.83. This value is rounded up to 3.

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