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## Frequency distribution: The organization of the data pertaining to a quantitative phenomenon involves the following four stages: - The set or series of individual observations - unorganized (raw) or organized (arrayed) data. - Discrete or ungrouped frequency distribution. - Grouped frequency dis...

## Frequency distribution: The organization of the data pertaining to a quantitative phenomenon involves the following four stages: - The set or series of individual observations - unorganized (raw) or organized (arrayed) data. - Discrete or ungrouped frequency distribution. - Grouped frequency distribution. - Continuous frequency distribution. ### Array: A better presentation of the raw date would be to arrange them in an ascending or descending order of magnitude, which is called the 'arraying' of the data. However, this presentation (arraying), though better than the raw data does not reduce the volume of the data. ### Discrete or ungrouped frequency distribution: A much better way of the representation of the data is to express it in the form of discrete or ungrouped frequency distribution where count the number of times each value of the variable occurs in the data. This is facilitated through the technique of tally bars. If the variables takes the values in a wide (jange) range then the data still remain unwieldy and need further processing for statistical analysis. #### Example 1: Following data shows the total number of overtime hours worked for 30 consecutive weeks by machinists in a machine shop. The displayed are in raw form: 91 89 88 89 90 92 86 88 87 85 88 87 90 87 91 89 92 89 88 90 85 84 86 84 91 87 85 90 89 92 #### Represent the above information by appropriate frequency distribution. **Solution:** - Variable (X): Number of overtime hours per week - Frequency(): Number of weeks, N = no. of weeks = 30 - Maximum observation: 92, Minimum observation: 84 ### Grouped frequency distribution: If the identity of the data values is not relevant, nor is the order in which the values occur, we can group the data into different classes (or class intervals) by dividing the range of values into a number of groups called classes and then recording the number of individual observations ( frequency), whose values fall into which the values of the variable are placed. The length of each interval is called the width of the classes. The lower limit of each class interval is called the upper class limit and the upper limit of each class interval is called the lower class limit. This form can be used for discrete variable. #### Example A computer company received a rush on orders during a particular period. Company records provide the following number of computers shipped per day during this period: 22 65 65 67 55 50 65 83 33 41 49 28 55 61 #### Represent the above information by appropriate frequency distribution. **Solution:** - Variable: Number of computers shipped per day - Frequency: Number of days #### Grouped frequency distribution of computers shipped per day | Classes | Frequency | |:---|:---| | 22-32 | 2 | | 33-43 | 3 | | 44-54 | 1 | | 55-65 | 5 | | 65-76 | 2 | | 77-87 | 1 | | Total | 14 | ### Continuous frequency distribution: In some cases, it may be necessary to convert the data into a grouped frequency distribution with continuous class intervals like 0-10, 10-20, 20-30, etc. In this case, the class intervals are continuous but we consider the corresponding frequencies is known.