 Hello and welcome to the session. In this session we will discuss data handling. Data is usually collected in the context of a situation that we want to study. The data that we collect is represented graphically in different ways like we can represent the data graphically using a pictograph. It is a pictorial representation of data using symbols. Like suppose this symbol represents 10 apples. Then according to this pictorial representation we have that this row represents 30 apples. Since we have 3 symbols and one symbol denotes 10 apples. So this would mean 30 apples and this row would mean 50 apples. Since there are 5 symbols in this and one symbol stands for 10 apples. Next we are representing the data graphically is using a bar graph. Basically a bar graph is a display of information using bars of uniform width. Their heights being proportional to the respective values. This is a bar graph which shows the usage of different modes of transport that is car versus auto cycle by students of a school. So according to this we have that the number of students using car as the mode of transport is 5, bus as the mode of transport are 10, auto as the mode of transport are 15, then cycle as the mode of transport are 5. Here as you can see that the bars are of equal width with equal gaps in between and the bar heights give the quantity for each category. Now the third way of representing the data graphically is using a double bar graph. It is a bar graph showing sets of data simultaneously and it is basically used for comparison of data. Consider this, this is a double bar graph. It is showing the usage of the mode of transport by the students of a school in two different years that is in the year 1995 and in the year 1996. The shaded bars represent the year 1996 and the bars which are not shaded represent the year 1995. So let's try reading this double bar graph. According to this we have that the number of students using car as the mode of transport in the year 1995 are 5 and in the year 1996 it's 10. Then in the year 1995 the number of students using bus as the mode of transport are 10 and in the year 1996 it's 15. Then for auto the number of students are 5 in the year 1995 and in the year 1996 it's 15. Then for cycle the number of students are 5 in the year 1995 and 10 in the year 1996. So this is the double bar graph. Next we discuss organizing data. Data mostly available to us in an unorganized form is called raw data. If we need to get some meaningful information from this data that we collect we need to organize the data systematically. Next we discuss the favorite routes from the group of students and this is the data that was collected from that survey. Let's arrange this data using tally marks. Now we have made this table to organize or you can say to represent this data in a systematic manner using tally marks. The number of students who prefer eating apple as you can see are 4. So we would put 4 tally marks and the frequency is 4. Then the number of students who prefer eating orange are 3. So there would be 3 tally marks and the frequency is 3. And the number of students prefer eating grapes are 3. So there would be 3 tally marks and the frequency is 3. The number of tallys before each fruit gets the number of students who like eating that fruit. Now we have that frequency gives the number of tines that a particular entry occurs. This column as you can see shows the frequency and this table that we have made is known as frequency distribution table. Next we discuss grouping data. The raw data that we get can be grouped and presented systematically using a grouped frequency distribution. Sometimes when we have to deal with a large data then we make groups of observations that is we group the data and we make distribution which is known as grouped frequency distribution. So let us see how we do this. These are the marks obtained by a group of students in English. Now we arrange this data or we make groups of this data that we have collected. So we have made 3 groups 0 to 10, 10 to 20 and 20 to 30. Now from this data let's see how many observations fall under each category of marks. So the number of students getting the marks between 0 to 10 are given by 4. So there would be 4 tally marks and the frequency is written as 4. Then the number of students getting the marks between 10 to 20 are given by 3. So there would be 3 tally marks and the frequency is 3. The number of students getting the marks between 20 to 30 are given by 3. So there would be 3 tally marks and the frequency is 3. So this is how we can group the data and this distribution that we obtain is known as grouped frequency distribution. Now each of these groups that is 0 to 10, 10 to 20, 20 to 30 are called class interval or you can simply say class. Each class interval has the upper limit and the lower limit like for the class interval 0 to 10 the 0 would be the lower limit and 10 is the upper limit. In the same way we can find the lower and upper limits for the other class intervals and the difference between the upper class limit and lower class limit is called the width or the size of the class interval. Like if you consider the interval 0 to 10 in this the difference of the upper limit and the lower limit that is 10 minus 0 is equal to 10 is the width of the class interval 0 to 10 or you can say size of the class interval 0 to 10. Next we have bars with a difference. Group data can be presented using a histogram. Let's see what is a histogram. It is a type of bar diagram where the class intervals are shown on the horizontal axis and the heights of the bar show the frequency of the class interval. Consider this group frequency distribution which showed the marks of the students in English subject. Now let's represent this data using histogram. So we have taken the marks on the X axis and the scale that we have taken on the X axis is 1 unit represents 10 marks and we have taken the number of students on the Y axis and the scale on the Y axis that we have taken is 1 unit represents 1 student. According to this table we have that the number of students getting the marks between 0 to 10 are 4 that is the frequency is 4. So for this interval 0 to 10 we will make a rectangle or a bar of length 4 in this way. So this rectangular bar shows that the number of students getting the marks between 0 to 10 are 4. In the same way we will make the rectangular bars for the other groups of marks. So as you can see we have drawn the other rectangular bars also. So we say that the number of students getting the marks between 0 to 10 are 4, number of students getting the marks between 10 to 20 are 3 and the number of students getting the marks between 20 to 30 are 3. So this is how we represent a group frequency distribution using a histogram. Now as you can see the bars are of equal width with no gaps in between and the height of the bar gives the number of data items in a particular group and is the frequency. Consider the histogram in this you can see this line. This is called the drag line. It is used along the horizontal line to indicate that we are not showing the numbers between 0 to 10. So this completes this session. Hope you have understood the graphical representation of data using a pictograph, bar graph and a double bar graph and how we organize the data, how we make the frequency distribution table and how we make a histogram.