FREQUENCY DISTRIBUTION.pptx

Frequency distribution, types of frequency distribution.
Ungrouped frequency distribution
Grouped frequency distribution
Cumulative frequency distribution
Relative frequency distribution
Relative cumulative frequency distribution
Graphical representation of frequency distribution
I. Representation of Grouped data
1.Line graphs
2.Bar diagrams
a) Simple bar diagram
b)Multiple/Grouped bar diagram
c)Sub-divided bar diagram.
d) % bar diagram
3. Pie charts
4.Pictogram
II. Graphical representation of ungrouped data
1, Histogram
2.Frequency polygon
3.Cumulative change diagram
4. Proportional change diagram
5. Ratio diagram

1. BIOSTATISTICS AND RESEARCH METHODOLOGY Unit-1: frequency distribution PRESENTED BY Himanshu Rasyara B. Pharmacy IV Year UNDER THE GUIDANCE OF Gangu Sreelatha M.Pharm., (Ph.D) Assistant Professor CMR College of Pharmacy, Hyderabad. email: [email protected]

2. FREQUENCY DISTRIBUTION When observations, discrete or continuous are available on a single characteristic of a large number of individuals, often it becomes necessary to condense the data as far as possible without losing any information of interest. The frequency distribution is an example of such a data summary, a table/categorisation of the frequency of occurrence of variables in various class intervals. Sometimes a frequency distribution of a set of data is simply called a “Distribution”. For a sampling of continuous data, in general a frequency distribution is constructed by classifying the observations (variables) into a number of discrete intervals. For categorial data, frequency distribution is simply a listing of number of observations in each class or category, such as 20 males and 30 females entered in a clinical study. A frequency distribution can be graphed as a histogram or pie chart.

3. TYPES OF FREQUENCY DISTRIBUTION

4. 1. Ungrouped Frequency Distribution: Used for discrete variables. Also called “RAW DATA”. Includes data that has not been organised into groups like gender, martial status, types of family. DATA FREQUENCY 2 8 3 4 5 6 7 7 8 2 9 5 2. Grouped Frequency Distribution: They have class intervals. It includes data that has been organised into groups(into a frequency distribution) It is used if variables are continuous such as age, salary, body temperature, etc. DATA FREQUENCY 2-4 5 5-7 6 8-10 10 11-13 8 14-16 4 17-19 3 3. Cumulative Frequency Distribution: These are used to determine the number of observations that lie above/below a particular value in a data set. It also helps us to observe and understand how the values within a particular data set changes.

5. 4. Relative Frequency Distribution: It shows the proportion of the total number of observations associated with each value/class of values and is related to a probability distribution. 5. Relative Cumulative Frequency Distribution: It is a tabular summary of a set of data showing the relative frequency of items less than or equal to the upper class limit of each class. It is the fraction or proportion of the total number of items. C.I Frequency Cumulative Frequency Relative Frequency Cumulative Relative Frequency 60-64 1 1 1/25= 0.04 0.04 65-69 1 1+1=2 1/25= 0.04 0.04+0.04=0.08 70-74 2 2+2=4 2/25= 0.08 0.08+0.08=0.16 75-79 6 4+6=10 6/25= 0.24 0.16+0.24=0.4 80-84 3 10+3=13 3/25= 0.12 0.4+0.12=0.52 85-89 5 13+5=18 5/25= 0.2 0.52+0.2=0.72 90-94 5 18+5=23 5/25= 0.2 0.72+0.2=0.92 95-99 2 23+2=25 2/25= 0.08 0.92+0.08=1 Σ f= 25

6. GRAPHICAL PRESENTATION OF FRQUENCY DISTRIBUTION

7. I. LINE GRAPHS Line graphs are simple mathematical graphs that are drawn on the graph paper by plotting the data concerning one variable on the horizontal x- axis and other variable of data on the vertical y- axis.

8. II. BAR DIAGRAM Used for comparison of Quantitative data. Types of Bar diagram

9. 1. Simple Bar Diagram

10. 2. Multiple/Grouped Bar Diagram It is use when a number of items are to be compared in respect of two, three or more values. In this case the numerical values of major categories are arranged in ascending or descending order so that the categories can be readily distinguished. Different shades/colours are used for each categories.

11. 3. Sub Divided/Component Bar Diagram It is formed by dividing a single bar into several component parts. A single bar represents the aggregate value whereas the component parts represent the component values of the aggregate value.

12. 4. % Sub Divided Bar Diagram A sub-divided bar is drawn on a percentage basis. To draw a sub-divided bar chart on a percentage basis, we express each component as the percentage of its respective total. The diagram so obtained is called a percentage component bar chart or percentage stacked bar chart.

13. III. PIE CHART(Circular or Sector Chart) A pie chart is a circular graph which represents the total value with its components. The area of a circle represents the total value and the different sectors of the circle represents the different parts. The circle is divided into sectors by Radii and the areas of the sectors are proportional to the angles at the centre. In pie chart, data is expressed as Percentage.

14. IV. PICTOGRAM It is a way of representing statistical data in pictures. In this a number of pictures of same size and equal in value are drawn. Each pictures represents a number of units. The chief advantage of this method is it presents data in a very attractive way.

15. I. HISTOGRAM A histogram is a graph containing a set of rectangles, each being constructed to represent the size of the class interval by its width and the frequency in each class interval by its height.

16. II. FREQUENCY POLYGON It is a curve obtained by joining the middle points of the tops of the rectangles in a histograms by straight lines. It is used in a frequency distribution in which the class intervals are equal.

17. III. Cumulative Change Diagram (OGIVE) It is a graph which represent the data of the cumulative frequency distribution. It is used to find median, quartites, deciles, and percentiles. It is also used to find the number of observations which are expected to lie between two given values.

18. IV. PROPORTIONAL CHANGE DIAGRAM These are the relationships between two variables where their ratios are equivalent. (OR) In a proportional relationship one variable is always a constant value times the other. The process of calculating percentage may become very time consuming.

19. V. RATIO DIAGRAM This diagram has the added advantage that both relative and absolute changes can be determined from it. The bases of the construction is the use of a special paper known as “Arithlog or Ratio Paper”. It is provided in various sizes. It can not be easily understood by an untrained person.