A frequency distribution can be defined as the number of observations
falling into each of several ranges of values. It can be represented as
frequency tables, histograms. Either the percentage of observations or
the actual number of observations falling in each range can be
represented by Frequency Distribution. If the Frequency distribution
shows the percentage of observation then it is said to be Relative
frequency distribution.
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In statistics Frequency distribution plays a huge role and it can be represented either in a tabular or graphical format and it displays the number of observation within a given interval.
A frequency distribution can be represented by a histogram or pie chart. In case of large data sets, the stepped graph is approximated by the smooth curve of a distribution function which is known as a density function.
Frequency distribution mostly used for assigning probabilities and summarizing large data sets.
It is a method of representing unorganized data e.g. to show results of an income of people for a certain region, election, sales of a good within a certain period, etc.
Histograms:
The histogram is nothing but a summary graph representing a count of the data’s falling in various ranges. The groups of data are known as classes; here in histogram they are called as classes.
In mathematical sense, generally a histogram can be defined as a function Xi that counts the number of observations or data’s that fall into each of the bins. The graph of a histogram is similar to the one way to represent a histogram.
If,
n = number of observations and
k = total number of classes then, the histogram meets the following criteria.
n= `sum_(i=1)^k` Xi
Histograms can be defined as follows,
The lists ordered by quantity which shows the number of times each value appears is known as Univariate frequency distributions.
Example 1:
If 200 people rate a product assessing their agreement with a statement on the product on which ‘A’ indicates strong agreement and ‘E’ strong disagreement, the frequency distribution of their responses can be given as follows:
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Example 2:
The weight of the students in a class could be represented into the following frequency table:
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In statistics Frequency distribution plays a huge role and it can be represented either in a tabular or graphical format and it displays the number of observation within a given interval.
A frequency distribution can be represented by a histogram or pie chart. In case of large data sets, the stepped graph is approximated by the smooth curve of a distribution function which is known as a density function.
Frequency distribution mostly used for assigning probabilities and summarizing large data sets.
It is a method of representing unorganized data e.g. to show results of an income of people for a certain region, election, sales of a good within a certain period, etc.
Frequency distribution in histograms
Histograms:
The histogram is nothing but a summary graph representing a count of the data’s falling in various ranges. The groups of data are known as classes; here in histogram they are called as classes.
In mathematical sense, generally a histogram can be defined as a function Xi that counts the number of observations or data’s that fall into each of the bins. The graph of a histogram is similar to the one way to represent a histogram.
If,
n = number of observations and
k = total number of classes then, the histogram meets the following criteria.
n= `sum_(i=1)^k` Xi
Histograms can be defined as follows,
- In statistics, it is a pictorial representation of table frequencies, shown as bars. The diagram shows what proportion of cases fall into each of several categories. Simply Histogram is a form of data binning.
- Histogram is a bar chart representing the frequency distribution of values along a spectrum of possible values.
- Histograms are mainly used for density estimation.
Sample Problems
Univariate frequency tables:The lists ordered by quantity which shows the number of times each value appears is known as Univariate frequency distributions.
Example 1:
If 200 people rate a product assessing their agreement with a statement on the product on which ‘A’ indicates strong agreement and ‘E’ strong disagreement, the frequency distribution of their responses can be given as follows:
Number
|
Degree of agreement
|
Rank
|
| 60 | Strongly agree | A |
| 40 | Agree somewhat | B |
| 30 | Not sure | C |
| 40 | Disagree some what | D |
| 30 | Strongly Disagree | E |
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Example 2:
The weight of the students in a class could be represented into the following frequency table:
| Weight range (Kg's) | Number of students | Cumulative number |
| 40 -50 | 25 | 25 |
| 50-55 | 35 | 60 |
| 55-60 | 15 | 75 |
| 60-65 | 24 | 99 |
| 65-70 | 10 | 109 |
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