Group-4-Report-Frequency-Distribution.ppt
- 2. Objectives • Define Frequency Distribution • Identify the Parts of the Frequency Table • Organize data using Frequency Distribution • Represent data in Frequency Distribution graphically using Histograms, Frequency Polygons and Ogives
- 3. Introduction Statistics is of vital importance in vast variety of fields. It's obvious that society can’t be run effectively on the basis of hunches or trial and error, and that in business and economics much depend on the correct analysis of numerical information. Decisions based on data will provide better results than those based on intuition or gut feelings.
- 4. Introduction Statistical thinking permeates all social interaction. For example, take these questions: • ‘Which university should I go to?’ • ‘Should I buy a new car or a second-hand one?’
- 5. Introduction • ‘Should the company buy this building or just rent it?’ • ‘Should we invest now or wait till the new financial year?’ • ‘When should we launch our new product?’
- 6. Introduction All of these require decisions to be made, all have costs and benefits, all are based upon different amounts of data, and all involve or necessitate some kind of statistical calculation. This is where an understanding of statistics and knowledge of statistical techniques will come in handy.
- 7. Frequency Distributions Frequency Distribution is the basic building block of statistical analytical methods and the first step in analyzing survey data. It helps researchers organize and summarize the survey data in a tabular format, interpret the data and detect extreme values in the survey data set.
- 8. Frequency Distributions • When data are collected in original form, they are called Raw Data. • When the raw data is organized in table form, using classes and frequencies, it becomes Statistical Data using Frequency Distribution functions. • When raw data is organized into frequency tables it now becomes Information.
- 10. Types of Frequency Distributions • Categorical Frequency Distributions - can be used for data that can be placed in specific categories, such as nominal- or ordinal-level data. • Examples - political affiliation, religious affiliation, blood type etc.
- 11. Blood Type Frequency Distribution Example Class Frequency Percent A 5 20 B 7 28 O 9 36 AB 4 16
- 12. Ungrouped Frequency Distributions • Ungrouped Frequency Distributions - can be used for data that can be enumerated and when the range of values in the data set is not large. • Examples - number of miles your instructors have to travel from home to campus, number of girls in a 4- child family etc.
- 13. Number of Miles Travelled Example Class Frequency 5 24 10 16 15 10
- 14. Grouped Frequency Distributions • Grouped Frequency Distributions - 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.
- 15. Lifetimes of Boat Batteries Example Class limits Class Boundaries Cumulative 24 - 37 23.5 - 37.5 4 4 38 - 51 37.5 - 51.5 14 18 52 - 65 51.5 - 65.5 7 25 frequency Frequency
- 16. Parts of Frequency Table • Class Limits groupings or categories defined by lower and upper limits • Lower Class Limits are the smallest numbers that belongs to the different classes. • Upper Class Limits are the highest numbers that belongs to the different classes.
- 17. Lifetimes of Boat Batteries Frequency Table • Class Limits represent the smallest and largest data values that can be included in a class. • In the lifetimes of boat batteries example, the values 24 and 37 of the first class are the class limits. • The lower class limit is 24 and the upper class limit is 37.
- 18. Lifetimes of Boat Batteries Frequency Table Class Limits Frequency 24-37 4 38-51 14 52-65 7 Lower Class Limits
- 19. Lifetimes of Boat Batteries Frequency Table Class Limits Frequency 24-37 4 38-51 14 52-65 7 Upper Class Limits
- 20. Parts of Frequency Table • The class boundaries are used to separate the classes so that there are no gaps in the frequency distribution.
- 21. Class Boundaries • Steps to calculate class boundaries: 1. Subtract the upper class limit for the first class from the lower class limit for the second class. 38-37 = 1 2. Divide the result by two. 1÷2 = 0.5
- 22. Terms Associated with a Grouped Frequency Distribution 3. Subtract the result from the lower class limit and add the result to the upper class limit for each class. Class Limits Class Boundaries Frequency 24-37 23.5-37.5 4 38-51 37.5-51.5 14 52-65 51.5-65.5 7
- 23. Parts of Frequency table • The class midpoint a point that divides a class into two equal parts. This is the average of the upper and lower class limits. Class Limits Midpoint Frequency 24-37 30.5 4 38-51 44.5 14 52-65 58.5 7
- 24. Parts of Frequency Table • The class width for 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. Class Limits Frequency 14 24-37 4 14 38-51 14 14 52-65 7 Class Width
- 26. Relative Frequency Distribution Class Limits Relative Frequency 24-37 16% 38-51 56% 52-65 28% Class Limits Frequency 24-37 4 38-51 14 52-65 7 Total Frequency = 25 4÷25 = 0.16 14÷25 = 0.56 7÷25 = 0.28 Relative Frequency Table
- 27. Types of Frequency Distribution • Cumulative Frequency Distribution is used to determine how many or what proportion of the data values are below or above a certain value. • To create a cumulative frequency polygon, scale the upper limit of each class along the x-axis and corresponding cumulative frequency along the y-axis
- 28. Cumulative Frequency Distribution Class Limits Upper Limit Frequency Cumulative Frequency 24-37 37 4 4 38-51 51 14 18 ( 4+14) 52-65 65 7 25 ( 18+7) Cumulative Frequency Table
- 29. Guidelines for 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.
- 30. Guidelines for Constructing a Frequency Distribution • The classes must be continuous. • The classes must be exhaustive. • The class must be equal in width.
- 31. Procedure for Constructing a Grouped Frequency Distribution • Find the highest and lowest value. • Find the range. • Find the number of classes by using k= 1+3.322log N. Round-up your answers. • Find the width by dividing the range by the number of classes and rounding up.
- 32. 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.
- 33. 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.)
- 34. 10 8 6 14 22 13 17 19 11 9 18 14 13 12 15 15 5 11 16 11 Grouped Frequency Distribution Example
- 35. 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.
- 36. 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.
- 37. • Step 5: Select a starting point for the lowest class limit. For convenience, this value is chosen to be 5, the smallest data value. The lower class limits will be 5, 8, 11, 14, 17 and 20. Grouped Frequency Distribution Example
- 38. • Step 6: The upper class limits will be 7, 10, 13, 16, 19 and 22. For example, the upper limit for the first class is computed as 8 - 1, etc. Grouped Frequency Distribution Example
- 39. • Step 7: Find the class boundaries by subtracting 0.5 from each lower class limit and adding 0.5 to the upper class limit. Grouped Frequency Distribution Example
- 40. • Step 8: Tally the data, write the numerical values for the tallies in the frequency column and find the cumulative frequencies. • The grouped frequency distribution is shown on the next slide. Grouped Frequency Distribution Example
- 41. Class Limits Class Boundaries Frequency Cumulative Frequency 05 to 07 4.5 - 7.5 2 2 08 to 10 7.5 - 10.5 3 5 11 to 13 10.5 - 13.5 6 11 14 to 16 13.5 - 16.5 5 16 17 to 19 16.5 - 19.5 3 19 20 to 22 19.5 - 22.5 1 20 Note: The dash “-” represents “to”.
- 42. Visualizing Data • The three most commonly used graphs in research are: • The histogram. • The frequency polygon. • The cumulative frequency graph, or ogive (pronounced o-jive).
- 43. Visualizing Data • The histogram is a graph that displays the data by using vertical bars of various heights to represent the frequencies.
- 45. Visualizing Data • A frequency polygon is a graph that displays the data by using lines that connect points plotted for frequencies at the midpoint of classes. The frequencies represent the heights of the midpoints.
- 46. Example of a Frequency Polygon
- 47. Visualizing Data • A cumulative frequency graph or ogive is a graph that represents the cumulative frequencies for the classes in a frequency distribution.
- 48. Example of an Ogive 26 23 20 17 14 11 8 5 2 20 10 0 Number of Cigarettes Smoked per Day Cumulative Frequency Ogive
- 49. Other Types of Graphs • Time series graph - A time series graph represents data that occur over a specific period of time.
- 51. Pie Graph • Pie graph - A pie graph is a circle that is divided into sections or wedges according to the percentage of frequencies in each category of the distribution.
- 52. Pie Graph Robbery (29, 12.1%) Rape (34, 14.2%) Assaults (164, 68.3%) Homicide (13, 5.4%) Pie Chart of the Number of Crimes Investigated by Law Enforcement Officers In U.S. National Parks During 1995
- 53. Summary In this discussion, we present the difference between raw data and frequency distribution that sometimes gives us confusion. We also show how data can be group for easier analysis. There we have categorical frequency distribution, ungrouped frequency distribution and the most challenging among the three the grouped frequency distribution.
- 54. Summary After grouping the data, frequency polygon, histogram, ogive and other graphical techniques are used to present them in an effective and memorable way. Gathered facts or data are not enough in measuring reliability for a certain research. Thus, tabular or graphical representations make visual comparison of data easier and give a more lasting impression than is possible by any other means.
- 55. Assessment • Outpatient wait time: Waiting times (minutes) for 25 patients at a public health clinic are: 35 22 63 6 49 19 16 31 24 29 23 32 72 13 51 45 77 16 33 55 10 42 28 72 13 • Create a frequency distribution table with frequency, relative/percent frequencies, cumulative frequencies. Construct a histogram, frequency polygon and ogive.
- 56. “Statistics can be made to prove anything – even the truth.” – Anonymous
- 57. Group 4 FRANZ GELECA C. CARRANZA BERNADETTE MONTILLA JOAN J. PRINCIPE BERVERLY BARRUN RUBY JHANE FLORES MARIE SEDICOL DOMINGO ESPARES JR. JOHN MARK RECTO THANK YOU.