In the previous section we saw how the 'equal intervals' are formed in the 'Electricity bill analysis problem'. Now we will form the frequency distribution table, based on these intervals.
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| Fig.1.16 Table for making ordered list |
• Take the first entry. It is 224.
• Find the interval in which 224 will fall. It is 200 - 250.
• Put a '|' mark on the second column 'in line' with this interval. This is shown in the fig.1.17 below:
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| Fig.1.17 Tally mark for the first entry |
Repeat the process:
• Take the second entry. It is 94.
• Find the interval in which 94 will fall. It is 50 - 100.
• Put a '|' mark on the second column 'in line' with this interval. This is shown in the fig.1.18 below:
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| Fig.1.18 Tally mark for the second entry |
In this way, all the entries in the raw data list should be marked in the second column. Then the no. of tally marks can be counted and entered in the third column. The completed table is shown below:
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| Fig.1.19 Completed Table |
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| Fig.1.20 Pictorial representation |
The above fig.1.20 gives a better presentation of the results of analysis. Each interval in the table is represented by a rectangle. The heights of the rectangles gives us the frequency of that interval. We can see that
• The interval 200 – 250 has the most frequency. This means that, the 'number of houses whose bill amount falls between 200 and 250' is more in that locality.
• The number of houses which has very low bill amounts (less than 100) is less in that locality
• The number of houses which has very high bill amounts (greater than 350) is also low in that locality.
• Most of the houses have a bill amount between 150 and 350.
Now let us see some important features of the 'methods of organising data' that we saw so far:
• Type of Table
♦ The type of table shown in fig.1.7 in which each of the values in the raw data list is given a unique row is called Discrete frequency distribution table. The pictorial representation of this table is called Bar graph. In the Bar graph, each of the values in the raw data list is given a unique bar. (However, repeating values will be having a single common row and a single common bar.)
♦ The type of table shown in fig.1.19 above, in which the values in the raw data list are grouped is called a Grouped frequency distribution table.
• Pictorial representation
♦ The pictorial representation of a Discrete frequency distribution table is called a Bar graph
♦ The pictorial representation of a Grouped frequency distribution is called a Histogram
• The intervals (shown in the first column) in a grouped frequency distribution table are called class intervals (or simply 'class'). For example, 150 – 200 in fig.1.19 is a class interval.
• Every class interval has a lower class limit and an upper class limit. For example, in the class interval 300 – 350, 300 is the lower class limit. And 350 is the upper class limit.
• The difference between the upper class limit and the lower class limit is called the width or size of the class interval. And the widths of all the class intervals in a grouped frequency distribution table should be the same.
• The class intervals should be continuous. That is., the upper class limit of one class interval should be the lower class limit of the next higher class interval. The importance of such a rule can be explained with the help of examples:
Example of a continuous class interval sequence: 0 – 20, 20 – 40, 40 – 60, . . . etc.,
Example of a non-continuous class interval sequence: 0 – 20, 21 – 40, 41 – 60, . . . etc.,
If in the raw data list, there is a value 20.4, we cannot put it in any of the non-continuous class intervals. Because, in the class 0 - 20, no values greater than 20 can be put, and in the class 21 - 40, no values less than 21 can be put. In the continuous class interval sequence, it can be put in the interval 20 – 40. This will mean that there should be no gap between the rectangles in the Histogram.
Based on the above, another situation can arise. What if there is a value of 20? Two class intervals, 0 – 20, and 20 – 40 can accomodate 20. In such a situation, we adopt the convention that ‘the common value will belong to the higher class’. Thus, 20 will belong to 20 – 40 and not 0 – 20. Similarly, a value of 60 if present, will belong to 60 – 80 and not 40 – 60.
Based on the above discussions, we will see some solved examples in the next section.
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