Definition “The process of dividing a set of observation or objects into classes or Group.” One way classification Two way classification A manifold or cross classification
TO reduce the Large sets………. To display points of similarity………. To save mental strain by eliminating……… To reflect important aspects………… To prepare the ground for comparison…..
Classes should be arranged so that each observation can be placed in one and only one class . Classes should be inclusive. The conventional classification procedure should be adopted. The classification procedure should not be so elaborate.
TABULATIONSystematic presentation of data classified under suitable head and subheads and place in columns and rows
Title Column captions and boxhead Row captions and Stub Prefatory Notes and Footnotes Source Notes Body and arrangement of data Spacing and rulings
…….Title…… prefatory notesBoxhea Column captionsd units STUB …… ……. B D …… …… …. ... O Y …… …..FOOT NOTES……….SOURCE NOTES………..
Frequency: “ The number of observations falling in a particular class is referred to as the class frequency or simply “frequency” is denoted by f”
It is a tabular summary of a set of data that shows that frequency or number of data items that falls in each of several distinct classes or simply the arrangement of data according to magnitude is called frequency distribution.
The number or the values of the variables which describe the classes. Upper class limits Lower class limits
Upper class limits• Are the largest numbers that can actually belong to different classes 1-3 10 4-6 14 upper class limit 7-9 10 10-12 6 13-15 5 16-18 5
Lower class limits• Are the smallest numbers that can actually belong to different classes 1-3 10 4-6 14 Lower class limit 7-9 10 10-12 6 13-15 5 16-18 5
The class boundaries are the precise numbers which separate one class from another, the selection of these numbers removes the difficulty. If any ,in knowing the class to which particular value should be assighned e.g 0.5-3.5,3.5- 6.5,6.5-9.5 Class boundaries ( in Frequency miles) 0.5-3.5 10 3.5-6.5 14 6.5-9.5 10 9.5-12.5 6 12.5-15.5 5 15.5-18.5 5
Class midpoints• Midpoints of the classes• Class midpoints can be found by adding lower class limits to the upper class limits and dividing the sum by two.
Class midpoints• Midpoints of the classes Class limits( in miles) Frequency 123 10 456 14 Mid 789 10points 10 11 12 6 13 14 15 5 16 17 18 5
The class width of a class is equal to the differences b/w class boundaries. It can also be obtain by Difference b/w two successive lower and upper class limits. Difference b/w two successive class marks Denoted by h or c.
Decide on the number of classes into which the data are to be grouped. Determine the range variation in the data Divide the range variation by the number of classes to determine the approximate width or size of the equal class-interval
Decide where to locate the class limit of the lowest class and the lower class boundary. Determine the remaining class limit and class boundaries by adding the class-interval repeatedly. Distribute the data into appropriate classes. Total the frequency column to see that all the datas have been accounted for.
Twenty five army officers were given a blood test to determine their blood type.the data set is : A B B AB O O O B AB B B B O A O A O O O AB AB A O B A
It frequency distribution is: CLASS FREQUENCY A 5 B 7 O 9 AB 4 TOTAL 25 Now some general observations can be obtained from looking at the data in the form of frequency distribution. For example, the majority officers belonging to group O
Suppose a researchers wished to do a study on the number of miles that the employees of a large department store travelled to work each day.The researcher first would have to collect the data by asking each employee the approximate distance the store is from or his or her home.The data are: 1 2 6 7 12 13 2 6 9 5 18 7 5 3 15 15 4 17 1 14 4 16 4 5 8 6 5 18 5 2 9 11 12 1 9 2 10 11 4 10 9 18 8 8 4 14 7 3 2 6
It is very hard for us to tell the information from such a table full a raw data .Therefore the researcher organizes the data by constructing a frequency distribution. The frequency is the number of values in a specific class of distribution.
Graph Diagramssimple pie diagrams PictogramsComponentMultiple bar charts
A simple bar chart consist of horizontal or vertical bars of equal width and lengths proportional to the value they represent. Multiple Bar Chart To depict a number of related factors for comparison various years or at a number of places multiple bar diagrams.
When the magnitude of a factor is given with its sub factors , Each bar is further is sub divided into components in proportion to to the magnitude of the sub factors . It is also called sub-divided bars.
A popular device for portraying the statistical data by means of picture or small symbols. Pie diagrams A pie diagrams is a circle that is divided into sections according to the percentage of frequencies in each category of the distribution.
Time series historigram cumulative f polygon Histogram Frequency polygon
Graph present the data in a simple, clear and effective manner. facilitate comparison b/w two or more than two statistical series. It provide picture of a statistical series.
A curve showing changes in the value of one or more items from one period of time to the next is known as the graph of time series . This curve also called historigaram .
A histogram consist of a set of adjacent rectangles whose bases are marked off by class boundaries ( not class limit) on the X- axis and whose heights are proportional to frequencies associated with respective classes.
A frequency polygon is a graph that displays the data by using lines that connect points plotted for frequencies at the midpoints of classes. The frequencies represent the heights of midpoints .
When a frequency polygon or histogram is constructed over class midpoints make it sufficiently small for large number of observations, is smoothed. And shows a continuous curve it is called frequency curve.