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### Frequency distribution The organization of the data pertaining to a quantitative phenomenon involves the following four stages: 1. The set or series of individual observations - unorganized (raw) or organized (arrayed) data. 2. Discrete or ungrouped frequency distribution. 3. Grouped frequency...

### Frequency distribution The organization of the data pertaining to a quantitative phenomenon involves the following four stages: 1. The set or series of individual observations - unorganized (raw) or organized (arrayed) data. 2. Discrete or ungrouped frequency distribution. 3. Grouped frequency distribution 4. 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 date 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 (large) 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 97 85 88 87 85 88 87 90 87 91 89 92 89 88 90 86 84 86 84 91 87 85 90 89 92 ### Represent the above information by appropriate frequency distribution: Variable (X): Number of overtime hours per week Frequency (f): Number of weeks. N= no. of weeks = 30 Maximum observation: 92. Minimum observation: 84 ### Grouped frequency distribution: If the identification of each individual value is not relevant, nor is the order in which they occur, we can divide the data into different classes (or class intervals) by dividing the range of the data into a number of groups called classes and then recording the number of values of the variable are falling into which the values of the variable are falling into each class interval. This interval is called the width of the classes. The smallest value in a class interval is called the lower class limit and the largest value is called the upper class limit and should be taken in the inclusive form so that both upper and lower limits are at the same level. This procedure can be used for discrete variables. ### Example A computer company received a rush order for a computer system in a short period. Company records provide the following information about the number of computers shipped each day: 22 65 65 67 55 50 65 83 33 41 49 28 55 61 ### Represent the above information by appropriate frequency distribution: Variable: Number of computers shipped per day Frequency: Number of days