On many occasions, we may want to collect information and do an analysis of it. For example a Canteen manager in an University campus may want to know which flavours of ice cream are more popular among students. To find it, he sets about to 'collect the information'. The easiest way to do this is to ask the students themselves. So he meets each student and notes down their preferred flavour. The information that he collects on his note book may look like this:
Student 1: Strawberry, Student 2: Vanilla, Student 3: Chocolate, Student 4: Vanilla, Student 5: Butter scotch ..... Student 25: Chocolate.
He collected information from 25 students. Here, the details about students is not necessary. So he needs to note down the flavour only with a serial number. So the list will look like this:
1. Strawberry, 2. Vanilla, 3. Chocolate, 4. Vanilla, 5. Butterscotch, ....... 25. Chocolate.
The information collected in this way is called Data. By just looking at this list, we cannot arrive at a conclusion about the most preferred flavour. This is particularly so, if the list is large. As it is a random list, it is called Raw Data. The raw data will be taken from the 'field' (which is the University campus in our case), to the office. There it will be 'analysed' and made into suitable 'mathematical models'. By this process, many important conclusions can be made. We will now discuss the methods to make some simple and basic mathematical models from the raw data.
The first step is to make an 'ordered list' from the raw data. For this, a table is drawn up as shown in fig.1.1.
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| Fig.1.1 Table for making ordered list |
The first column shows the 'Flavour'. The second column shows the Tally marks. The third column shows the 'Number of students'. The first column is easy, and is already filled here. Let us now fill up the second column. For this the complete raw data collected from the 25 students is given below:
Based on this list, we now put the tally marks in the second column. The steps are as follows:
• Take the first entry in the raw data list. It is 'Strawberry'.
• Find 'Strawberry' in the first column.
• Put a '|' mark on the second column 'in line' with strawberry. This is shown in the fig.1.2.
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| Fig.1.2 Tally mark for the first entry in the Raw data list |
Repeat the process:
• Take the second entry. It is 'Chocolate'.
• Find 'Chocolate' in the first column.
• Put a '|' mark on the second column 'in line' with Chocolate. This is shown in the fig.1.3
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| Fig.1.3 Tally mark for the second entry in the data list |
Repeat the process:
• Take the third entry. It is 'Strawberry'.
• Find 'Strawberry' in the first column.
• Put a '|' mark on the second column 'in line' with Strawberry. This is shown in the fig.1.4.
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| Fig.1.4 Tally mark for the third entry in the data list |
In this way all the entries in the raw data should be marked in the 'Tally marks' column. For doing this, we must learn to do a 'special type of marking' when the count for an item reaches 5. It can be explained based on an example: After marking the 14 th item, the table will look like in fig.1.5.
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| Fig.1.5 Tally marks after the 14 th item |
Now take the 15 th item. It is Strawberry. Strawberry has been entered four times so far. The next one will be the fifth. For a fifth entry, we do not put a '|' mark. Instead, we put a diagonal '\' mark. This diagonal must cross all the four '|' marks. This is shown in the fig.1.6 below:
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| Fig.1.6 Diagonal Tally mark |
Now we can proceed to enter the rest of the items. The completed table is shown in fig.1.7 below:
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| Fig.1.7 Completed Table |
We can see that the last column shows the total number of students who prefer each flavour.
The counting of tally marks is made much easier by making the diagonal mark after four. Because each group with a diagonal will indicate a 'five'. So we do not have to count with in such groups.
Now let us see some features of the above table.
• The total number of times that a particular item (in our example, items are the 'flavours') occurs in the raw data is called the frequency of that item. For example, the frequency of chocolate is 6.
• The frequency is the 'total number' of a particular item. This 'total number' is distributed randomly in the raw data. So it is not so easy to get the frequency of a particular item from the raw data.
• But the table readily gives us the frequency of each item. So the table is called Frequency distribution table.
Now let us see another method to 'present' the information in the frequency distribution table. It is called the Bar graph. It is a pictorial representation of the 'results of the analysis'. The fig.1.8 shows the bar graph of our problem.
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| Fig.1.8 Bar Graph |
• Each item, is represented by a bar.
• The 'height of the bar' of an item is equal to it's frequency.
• The widths of all the bars are equal
• The width of all the gaps between the bars are equal.
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