# Frequency Distribution

**What is Frequency Distribution?
Ans. A frequency distribution is an orderly arrangement of data classified according to the magnitude of the observations. When the data are grouped into classes of appropriate size indicating the number of observations in each class we get a frequency distribution. By forming frequency distribution, we can summarize the data effectively. It is a method of presenting the data in a summarized form. Frequency distribution is also known as Frequency table.
**Uses of Frequency Distribution:-
1. Frequency distribution helps us to analyze the data.
2. Frequency distribution helps us to estimate the frequencies of the population on the basis of the ample.
3. Frequency distribution helps us to facilitate the computation of various statistical measures.
**Frequency Distribution Table:- Frequency distribution table (also known as frequency table) consists of various components.
Classes:A large number of observations varying in a wide range are usually classified in several groups according to the size of their values. Each of these groups is defined by an interval called class interval. The class interval between 10 and 20 is defined as 10-20.
Class limits:The smallest and largest possible values in each class of a frequency distribution table are known as class limits. For the class 10-20, the class limits are 10 and 20. 10 is called the lower class limit and 20 is called the upper class limit.
Class limit:Class limit is the midmost value of the class interval. It is also known as the mid value. $\text{Mid value of each class}$ =$\frac{(\text{lower limit + Upper limit})}{2}$.
If the class is 0-10, lower limit is 0 and upper limit is 10. So the mid value is
$\frac{(0 + 10)}{2}$ = $\frac{10}{2}$= 5.
Magnitude of a class interval:The difference between the upper and lower limit of a class is called the magnitude of a class interval.
Class frequency:The number of observation falling within a class interval is called class frequency of that class interval.
**There are many types of frequency distributions:-
1.Grouped frequency distribution
2.Ungrouped frequency distribution
3.Cumulative frequency distribution
4.Relative frequency distribution
5.Relative cumulative frequency distribution.
1. Relative Frequency Distribution:-
A relative frequency distribution is a distribution in which relative frequencies are recorded against each class interval. Relative frequency of a class is the frequency obtained by dividing frequency by the total frequency. Relative frequency is the proportion of the total frequency that is in any given class interval in the frequency distribution.
2. Cumulative Frequency Distribution:-
One of the important type of frequency distribution is Cumulative frequency distribution. In cumulative frequency distribution, the frequencies are shown in the cumulative manner. The cumulative frequency for each class interval is the frequency for that class interval added to the preceding cumulative total. Cumulative frequency can also defined as the sum of all previous frequencies up to the current point.
3. Cumulative Relative Frequency Distribution:-
Cumulative relative frequency distribution is one type of frequency distribution. The relative cumulative frequency is the cumulative frequency divided by the total frequency.
4. Simple Frequency Distribution:- Simple frequency distribution is used to organized orderly the larger data sets. When the number of cases being studied is large, it is inconvenient to list them separately because the list would be too long. A simple frequency distribution shows the number of times each score occurs in a set of data. To find the frequency for score count how many times the score occurs.
5. Grouped Frequency Distribution:-
A grouped frequency distribution is an ordered listed of a variable X, into groups in one column with a listing in a second column, the frequency column. A grouped frequency distribution is an arrangement class intervals and corresponding frequencies in a table.
There are certain rules to be remembered while constructing a grouped frequency distribution
1. The number of classes should be between 5 and 20.
2. If possible, the magnitude of the classes must be 5 or multiple of 5.
3. Lower limit of first class must be multiple of 5
4. Classes are shown in the first column and frequencies in the second column.
6. Ungrouped Frequency Distribution:-
A frequency distribution with an interval width of 1 is reffered to an ungrouped frequency distribution. Ungroped frequency distribution is an arrangement of the observed values in ascending order. The ungrouped frequency distribution are those data, which are not arranged in groups. They are known as individual series. When the ungrouped data are grouped, we get the grouped frequency distribution.
**Frequency Distribution Graph:- The graphs of frequency distribution are frequency graphs that are used to reveal the characteristicsof discrete and continuous data. Such graphs are more appealing to eye than the tabulated data. This helps us to facilitate comparative study of two or more frequency distributions. We can compare the shape and pattern of the two frequency distributions.
*The most commonly used graphs of frequency distribution are:-
1. Histogram
2. Frequency polygon
3. Frequency Curve
4. Ogives (Cumulative frequency curves).
***Mission Geography***