Biostatistics Frequency distribution
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Frequency distribution is a method to organize and summarize data by grouping it into intervals called classes. It displays how often observations from a sample fall into each class. To create a frequency distribution, one first determines the class intervals and then counts the frequency of observations in each interval. This information can be presented in a table or graphically as a line graph, bar graph, pie chart, or other visualizations. Frequency distributions provide a simplified view of the overall patterns in large data sets.
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Biostatistics Frequency distribution
- 1. Frequency distribution BY Dr. Aswartha Harinatha Reddy Bangalore
- 2. • Frequency is the number of times a character that has appeared in the collected data. • Frequency distribution is also known as Frequency table. • A frequency distribution is an orderly arrangement of data classified according to the size of the observations. • When the data are grouped into classes of appropriate size indicating the number of observations in each class we get a frequency distribution.
- 3. • By forming frequency distribution, we can summarize the data effectively. • It is a method of presenting the data in a summarized form.
- 4. Frequency distribution table (also known as frequency table) consists of various components. • Class interval : A large number of observations varying in a wide range are usually classified in several groups according to the size of their values. Each of these groups is defined by an interval called class interval. The class interval between 10 and 20 is defined as 10-20. Class limit: Class limit is the midmost value of the class interval. It is also known as the mid value.
- 5. Constructing frequency distribution table: Marks obtained by twenty students in a subject are: 15,18,25,26,18,32,15,25,25,22,25,25,02,32,22,10,24,18,20,26. Class intervals (Marks) Tally marks Frequency 1-10 II 2 11-20 IIIIII 6 21-30 IIIIIIIIII 10 31-40 II 2 Total 20
- 6. Steps in preparing a frequency distribution table: • The class intervals would be 1-10, 11-20, 21-30 and 31-40. • Count number of observations in each interval. • Read the list form left to right and place a tally marks in the row. • For example the first observation is 02 so place a tally mark in the row beside where 1-10 appears in class interval column. • Record tally marks in the final column called Frequency.
- 7. Relative frequency distribution: • The relative frequency is the fraction or proportion of the total number of items belonging to the class. • It is obtained by dividing the frequency of each class by the total number of observations. • Relative frequency of class= Frequency of class / Total frequency • R.F=f/∑f
- 8. Relative frequency distribution: • Find out the relative frequency distribution for the following data. • 5,15,7,38,14,13,12,22,33,24,34,36,27. Class intervals Frequency (f) Relative Frequency 1-10 2 2/13=0.153 11-20 4 4/13=0.307 21-30 3 3/13=0.230 31-40 4 4/13=0.307 Total ∑f =13 Relative frequency=0.997
- 9. Cumulative frequency distribution: • The cumulative frequency for a specific value in a frequency table is the sum of the frequencies for all values at or below the given value.
- 10. Cumulative frequency distribution: • Find out the cumulative frequency distribution for the following data. • 5,15,7,38,14,13,12,22,33,24,34,36,27. Class intervals Frequency (f) Cumulative Frequency 1-10 2 0+2=2 11-20 4 2+4=6 21-30 3 6+3=9 31-40 4 9+4=13 Total ∑f =13 Cumulative Frequency= 13
- 11. Graphical distribution of ungrouped data: • Data is often described as ungrouped or grouped. • Ungrouped data is data given as individual data points. • Ungrouped data is data given with out class intervals. • Ungrouped data without a frequency distribution.
- 12. Line graph: • Line graphs is the simplest way of diagrammatic representation of data. • In a vertical line graph, the frequency always goes on the vertical axis. • The scores (Class intervals) will be on the horizontal axis (x axis) and frequency on the vertical axis (Y axis). • Don't forget to label both axes and give the graph a title.
- 13. • Line graphs used to represent data related to temperature, rainfall, population growth, birth rates and death rates during different periods.
- 14. Draw line graph following data: • 3, 7, 6, 2, 5, 9, 10, 8, 7,1, 8, 4,3, 5, 6, 7, 8, 7, 6, 5, 3, 6, 9, 8, 7, 5, 9, 6, 7, 8. • Produce a frequency table: Class intervals 1-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100 Class intervals or score
- 16. Bar graph: • A bar graph is a chart that uses bars to show comparisons between categories of data. • The bars can be either horizontal or vertical. • The height of bar represents the frequency of the corresponding observation.
- 17. Bar graph example: Activities Dance Music Art Cricket Football No. of Children 30 40 25 20 53 The following data gives the information of the number of children involved in different activities.
- 18. Pie chart: • It is a circular graph which is used to represent data. • In this various observations of the data are represented by the sectors of the circle. • The total angle formed at the centre is 360°. • The whole circle represents the sum of the values of all the components. • The angle of the observation is calculated by following equation:
- 19. Construction of pie chart/pie graph: The following table shows the numbers of hours spent by a child on different events on a working day. Activity No. of Hours School 6 Sleep 8 Playing 2 Study 4 T. V. 1 Others 3
- 20. Activity No. of Hours Measure of central angle School 6 (6/24 × 360)° = 90° Sleep 8 (8/24 × 360)° = 120° Playing 2 (2/24 × 360)° = 30° Study 4 (4/24 × 360)° = 60° T. V. 1 (1/24 × 360)° = 15° Others 3 (3/24 × 360)° = 45° The central angles for various observations can be calculated as: Total values: 24
- 22. Pictograms • Pictograms (often also known as “pictographs” or, as single units, “icons”) are essentially images that are used to represent data. • They are usually a simplified representation of a concept, with a unicolored flat design. OR • When statistical date is represented by pictures, they give a more attractive presentation. Such pictures are called PICTOGRAMS.
- 23. • A pictogram may also be used in subjects such as tourism, geography and in road maps.
- 24. • Number of children who eat different fruits
- 25. Cartogram: • When numerical facts are shown in form of maps is called cartograms. • These may be flow maps, thematic maps, dot maps.
- 26. Thematic maps
- 27. Flow maps
- 29. THANK YOU