In the previous post, we have discussed the concept of Tables and Tabulation of Variables in Statistics. Here we will discuss the concept of Statistical Tables better known as Frequency Distributions of Frequency Tables.
Statistical Tables
Ø There are different types of tables in statistics.
Ø The most common type of table in the statistics is ‘Frequency Table’ or ‘Frequency Distribution’.
Ø Frequency Distribution definition: “The frequencies of occurrence of data values are presented in tabular form in the ascending order of magnitude”.
Ø It is a statistical table that shows the frequency of various outcomes in a sample.
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Ø The frequency table shows the total for each category or group of data.
Example: A raw data and its frequency distribution is given below
Ø A frequency table composed of TWO components:
(1). Class
(2). Frequency
Class and Frequency
Ø When a population is divided into small groups on the basis of some attributes or characteristics, each such group is considered as a class.
Ø In each class, the number of individual value of that particular feature is one or many.
Ø Such occurrence of individuals in a class is called frequency.
Thus a Frequency Table is “the arrangement of distribution of individuals of a class which displays the frequency of the individuals according to a characteristic.”
How to construct a Frequency Distribution?
Ø For the construction of a frequency distribution, the class or class intervals are first decided.
Ø Class interval: ‘Class interval is the difference between the lower and upper-class limits’.
Ø The class interval is also called as bin or cell.
Ø First find the largest observation (value) in the data.
Ø Then find the smallest observation (value) in the data.
Ø Take the difference between largest and smallest observation.
Ø This value (difference between largest and smallest observation) is called the ‘range’.
Ø Fix the class interval or class width.
Ø For biological samples, 5 or 10, 20, 30, 40, 50 etc. are used as class intervals.
Ø The class interval is denoted as ‘c’.
Ø Total number of classes required for the data can be determined from the range.
Exercise: The following is the weight (in g) of fruits collected from an orchard. Prepare a frequency distribution of the raw data.
185, 303, 198, 201, 207, 213, 215, 218, 313, 226, 229, 231, 325, 236, 239, 241, 244, 248, 252, 256, 259, 262, 324, 340, 266, 180, 269, 271, 278, 280, 282, 285, 287, 290, 294, 295, 300, 190, 306, 308, 223, 317, 320, 321, 232, 326, 328, 332, 335, 338.
Solution:
Ø Largest observation in the data = 340
Ø Smallest observation = 180
Ø Difference between largest and smallest observation (range) = 340 – 180 = 160
Ø Let’s take the class interval as 40.
Ø Then number of classes required is:
Ø Classify the data
Classes in Frequency Distribution
Ø The class in statistics can be of two different types.
(1). Exclusive class
(2). Inclusive class
(1). Exclusive class:
Ø In exclusive type of class, the upper limit of a class and lower limit of the succeeding class will be the same.
Ø Here the lower limit is included whereas the upper limit is excluded.
Ø In the example, 00 is included but 10 is excluded.
Ø Exclusive classes are used to represent continuous variables.
(2). Inclusive class:
Ø In inclusive type of class, the upper limit of a class and the lower limit of the succeeding class will NOT be the same.
Ø Here both the upper and lower limits of the class are included.
Ø In the example, both 00 and 10 are included in the class.
Ø Inclusive classes are usually used to represent discrete variables.
Ø Further statistical analyses of frequency distribution, the inclusive classes are converted to exclusive type.
Ø This conversion is achieved by extending the class interval from both the ends.
Ø Example given below
Tally Mark Method
Ø For observing frequency, the commonly used method is “Tally Mark Method”.
Ø In tally mark method, we read each observation one by one and make a standing mark in the corresponding class.
Ø The fifth mark will be a cross mark which measures a unit of five observations.
Ø The total number of the marks in a particular class is its frequency.
Things to remember when constructing a frequency distribution:
Ø Every observation should find a place in one class or other.
Ø There should not be any overlapping of classes.
Ø Classes should be continuous, no gaps between the classes.
Ø As far as possible, the class intervals should be of same size.
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Ø The class interval should be selected in such a way that there should not be too less or too many classes.
Ø Usually, in biological samples, frequency tables with 5 to 15 classes are used.
Ø The classes and its nature should be self-explanatory.
Ø Classes should be either exclusive or inclusive, never mix both in a frequency distribution.
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Key questions
1. What is frequency distribution?
2. What are the components of frequency distribution?
3. Define Class
4. Define frequency
5. What is class interval?
6. Define range
7. How to calculate the number of class from range and class intervals
8. Differentiate Exclusive and Inclusive class.
9. Describe the ‘tally mark method’
10. What are the things to remember when constructing a frequency distribution?