Department of Animal Genetics & Breeding Veterinary College, Hebbal, Bangalore-24
Classification of Data And Frequency Distribution
Dr.R.Jayashree Assistant Professor
Definition Statistics may be defined as science of collection, presentation, analysis and interpretation of numerical data.
Process of arranging the data into groups or classes according to resemblance is called classification or grouping the given data into homogenous classes.
Dr R Jayashree, Asst Prof(AGB)
Objectives • Condense Voluminous raw data into simple acceptable form. • Eliminate unnecessary and unimportant elements • Facilitate comparison of data from different sources. • Have a birds eye view on data • Facilitate statistical treatment Dr R Jayashree, Asst Prof(AGB)
Types of Classification • • • •
Geographical: State, District Chronological: Year, Month Qualitative nature: Sex, Colour Quantitative nature: Milk Yield, Body weight Discrete
Continous
Dr R Jayashree, Asst Prof(AGB)
Quantitative Data Information resulting from measurable characteristics. Two Types 1. Discrete (discontinuous) data. A sample composed of the number of siblings of 10 students of a specific class: 3, 4, 1, 1, 3, 1, 0, 2, 1, 2 2. Continuous Data If we analyze the heights of the same students (cm):153, 157, 161, 160, 158, 155, 162, 156, 152, 159 Dr R Jayashree, Asst Prof(AGB)
Discrete Data A set of data is said to be discrete if the values / observations belonging to it are distinct and separate. That is, they can be counted (1,2,3,.......). For example, the number of kittens in a litter; the number of patients in a doctors surgery; the number of flaws in one meter of cloth; gender (male, female); blood group (O, A, B, AB). Dr R Jayashree, Asst Prof(AGB)
Continuous Data A set of data is said to be continuous if the values / observations belonging to it may take on any value within a finite or infinite interval. You can count, order and measure continuous data. For example: height; weight; temperature; the amount of sugar in an orange; the time required to run a mile. Dr R Jayashree, Asst Prof(AGB)
Qualitative Data These data represent the information concerning a quality, category or characteristic that cannot be measured but can be classified in various forms. Sex of animals, Body colour.
Dr R Jayashree, Asst Prof(AGB)
Frequency Distribution • • • •
Ordered array or organized data Un-grouped frequency distribution Grouped frequency distribution Continuous frequency distribution
Dr R Jayashree, Asst Prof(AGB)
Ordered array/organized data Arranging in ascending or descending order of magnitude also called arraying. Body Weight (Kg) of new born calves: 23, 20,21,25,26,29,20,19,22,25,27,19 Arrange these in ascending and descending order.
Dr R Jayashree, Asst Prof(AGB)
Discrete or ungrouped frequency distribution • Recorded as Tally marks of Tally –Scores • The number of times each value of variable is occurring is counted and recorded as Tally marks or Tally scores. Body Weight (Kg) of new born calves: 23,20,21,25,26,29,20,19,22,25,27,19,23,20,21,25, 26,29,20,19,22,25,27,19,20,21,25,26,29,20,19,22, 25,27,19,30,32,23,24,25,27,29,23,22,24,27,28. Dr R Jayashree, Asst Prof(AGB)
Body Weight (Kg) of new born calves: 23,20,21,25,26,29,20,19,22,25,27,19,23,20,21,25, 26,29,20,19,22,25,27,19,20,21,25,26,29,20,19,22, 25,27,19,30,30,23,24,25,27,29,23,22,24,27,28 •19 - | | | | | =6 •20 - | | | | | =5 •21 - | | |
=3
•22 - | | | | =4
25 - | | | | ||=7 26 - | | | =3 27 - | | | | =5 28 - | | =2 29 - | || =3 30 - || =2
•23 - | | | | =4 •24 - | | =2 Dr R Jayashree, Asst Prof(AGB)
Grouped frequency distribution • The data are classified into groups/classes by dividing the entire range of values of the variable into a suitable number of groups called class intervals and then recording the number of observation in each group/class interval.
Dr R Jayashree, Asst Prof(AGB)
Frequency Distribution
Class - The category
Frequency - Number in each class
Class limits - Boundaries for each class
Class interval - Width of each class
Class mark - Midpoint of each class
Dr R Jayashree, Asst Prof(AGB)
Frequency Distributions 1. Estimate the class interval- Stuger’s rule 2. Estimate Class Limit: The limit in which the class interval lies. (Upper limit and lower limit) 3. Find Class Frequency: The number of times a given value occurs. 4. Total frequency: The sum of class frequency. 5 Class width /size of the class interval: The difference between the upper and the lower limit Dr R Jayashree, Asst Prof(AGB)
Exercise-1 The following data refers to the body weight of 32 calves of 6 months age group and weights are as follows. 55, 60, 56, 45, 43, 47, 53, 54, 51, 52, 53, 60, 60, 46, 40, 55, 50, 75, 49,56,50,55,48,53,50,49,60, 52,53,72,65,58. Prepare an appropriate frequency table using the above data. Dr R Jayashree, Asst Prof(AGB)
Class Interval How to set the approximate number of classes to begin constructing a frequency distribution. Stuger’s rule K=1+3.322 Log10N K= Number of Class Intervals N= Total Frequency or total number of observations in the data. Dr R Jayashree, Asst Prof(AGB)
Class Interval for Exercise-1 K=1+3.322 Log10N N= 32 K=1+3.322 Log1032 K=1+3.322 (1.5051) K=5.8 approximately=6
Dr R Jayashree, Asst Prof(AGB)
Class width/Size of the class interval Range i= K Range= Highest Value in data- lowest value in data K= Class interval For the exercise:
75 − 40 i= 6
i= 5.8 approximately = 6 Dr R Jayashree, Asst Prof(AGB)
Class Limits • The limits in which a class interval lies. • Each class interval has upper and lower limit. Lowest value given =40 Class width =6 Class interval = 6
Dr R Jayashree, Asst Prof(AGB)
55, 60, 56, 45, 43, 47, 53, 54, 51, 52, 53, 60, 60, 46, 40, 55, 50, 75, 49,56,50,55,48,53,50,49,60, 52,53,72,65,58. Class Tally Interval marks Lowest value given =40 Class width =6 Class interval = 6
40-45
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46-51
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52-57
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58-63
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64-69
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70-75
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Dr R Jayashree, Asst Prof(AGB)
Class Frequency The number of times a given value occurs is the frequency of that value and known as class frequency. This is denoted by ‘f’. Inclusive method
Class Interval
Tally marks
Frequenc y
40-45
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3
46-51 52-57 58-63 64-69 70-75
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9 12 5 1 2
Dr R Jayashree, Asst Prof(AGB)
Total Frequency The sum of the class frequencies is known as the total frequency denoted by ‘N’
Class Interval
Tally marks
Frequency
40-45 46-51 52-57
||| |||| |||| |||| |||| ||
3 9 12
58-63 64-69 70-75
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5 1 2 N=32
Dr R Jayashree, Asst Prof(AGB)
Cumulative Frequency distribution It is obtained by adding frequencies of the succeeding class intervals of the distribution Class Interval
Tally marks
Frequency
40-45 46-51 52-57
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3 9 12
3 12 24
58-63 64-69 70-75
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5 1 2
29 30 32
Dr R Jayashree, Asst Prof(AGB)
Cummulative Frequency
Mid Point It is the value lying half way between the lower and upper class limits Lower limit of the class + Upper limit of the Class Midpoint = 2
Dr R Jayashree, Asst Prof(AGB)
Continuous Frequency Distribution While dealing with a continuous data it is not desirable to present the data into a grouped frequency distribution. For e.g. age structure of animals 2-4 years,4-6 years. In this upper limits are excluded from the respective classes are included in the immediate next class. These are termed as exclusive classes. Dr R Jayashree, Asst Prof(AGB)
Dr R Jayashree, Asst Prof(AGB)