Counting or measurements gives augment to raw data. Raw data itself is hard to understand as it lacks organization, summarization that renders it meaningless. Therefore, the raw data consists of to be put in some order via categorization and tabulation so as to decrease its volume and heterogeneity. To explain the conditions, draw conclusions or form inferences regarding events, the researcher should organize the data in certain meaningful manner. The most suitable process of organizing data is to form a frequency distribution.
The Frequency distribution:
The frequency is the number of occurrences of an element in a sample and is represented by f. A frequency distribution is the organization of raw data in a tabular form, by using classes and frequencies. If data are collected in original form, that is as observed or recorded they are termed as raw data.
Types of Frequency Distribution:
Two kinds of frequency distributions which are most frequently employed are the:
The absolute frequency is the number of times which a certain value comes into view in a statistical study.
It is represented by fi.
The sum of the absolute frequencies is equivalent to the total number of data, which is represented by N.
f1 + f2 + f3 +..... + fn = N
The relative frequency is stated as the quotient between the absolute frequency of a particular value and the total number of data.
This can be symbolized as a percentage and is represented by ni.
ni = fi/N
The total sum of the relative frequency is equivalent to 1.
The cumulative frequency is the total sum of the absolute frequencies of the entire values less than or equivalent to the value considered.
It is represented by Fi.
Ungrouped Frequency Distribution:
A frequency distribution having an interval width of 1 is termed to an ungrouped frequency distribution. Ungrouped frequency distribution is the arrangement of the observed values in ascending or increasing order. The ungrouped frequency distribution is those data, which are not ordered in groups. They are termed as individual series. If the ungrouped data are grouped, we obtain the grouped frequency distribution.
For illustration: A teacher conducted a test to a class of 26 students. The maximum mark is 5. The marks acquired by the pupils are:
3 2 3 3 4 3 1 2 5
1 5 4 2 1 1 3 3 4
1 2 1 4 5 4 2 2
We might arrange the marks in ascending or descending order. The data so symbolized is termed as an array.
1 1 1 1 1 1 1 2 2 2 2 2
3 3 3 3 3 3 4 4 4 4 4 4 5 5
The difference between the maximum and the minimum number is termed as the range of data. Therefore for the above data, the range is 5 - 1 which equivalents 4 marks.
Grouped Frequency Distribution:
A grouped frequency distribution is the organizing of raw data in tabular form, by employing classes and frequencies.
a) Determine the biggest and smallest values.
b) Calculate the Range = Maximum - Minimum
c) Choose the number of classes desired. This is generally between 5 and 20.
d) Find out the class width by dividing the range by the number of classes and rounding up.
e) Choose an appropriate starting point less than or equivalent to the minimum value. You will be capable to cover: 'the class width times the number of classes' values. You require covering one more value than the range.
f) To determine the upper limit of the first class, subtract one from the lower limit of the second class. Then carry on adding the class width to this upper limit to determine the rest of the upper limits.
g) Determine the boundaries by subtracting 0.5 units from the lower limits and adding 0.5 units from the upper limits. The boundaries are as well half-way between the upper limit of one class and the lower limit of the subsequent class. Based on what you are trying to achieve, it might not be essential to determine the boundaries.
h) Tally the data.
i) Find out the frequencies.
j) Determine the cumulative frequencies. Based on what you are trying to achieve, it might not be essential to determine the cumulative frequencies.
k) If required, determine the relative frequencies and/or relative cumulative frequencies.
Reasons for making a frequency distribution:
The major reasons for making a frequency distribution are as follows:
1) To sort out the data in a significant and intelligible manner.
2) To facilitate the reader to find out the nature and shape of the distribution.
3) To facilitate the computational methods to compute average and spread.
4) To allow the researcher to sketch charts and graphs for the presentation of data.
5) To allow the reader to make comparisons between various data sets.
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