Class 9 Presentation of Data

### Topic covered

color{red} ♦ Presentation of Data

### Presentation of Data

As soon as the work related to collection of data is over, the investigator has to find out ways to present them in a form which is meaningful, easily understood and gives its main features at a glance.

Let us now recall the various ways of presenting the data through some examples.
Q 3220678511

Consider the marks obtained by 10 students in a mathematics test as given below:
55 36 95 73 60 42 25 78 75 62
Class 9 Chapter 14 Example 1
Solution:

The data in this form is called raw data.
By looking at it in this form, can you find the highest and the lowest marks?
Did it take you some time to search for the maximum and minimum scores? Wouldn’t
it be less time consuming if these scores were arranged in ascending or descending
order? So let us arrange the marks in ascending order as

25 36 42 55 60 62 73 75 78 95

Now, we can clearly see that the lowest marks are 25 and the highest marks are 95.
The difference of the highest and the lowest values in the data is called the range of the
data. So, the range in this case is 95 – 25 = 70.

Presentation of data in ascending or descending order can be quite time consuming,
particularly when the number of observations in an experiment is large, as in the case
of the next example.
Q 3230678512

Consider the marks obtained (out of 100 marks) by 30 students of Class IX of a school:

Class 9 Chapter 14 Example 2
Solution:

Recall that the number of students who have obtained a certain number of marks is
called the frequency of those marks. For instance, 4 students got 70 marks. So the
frequency of 70 marks is 4. To make the data more easily understandable, we write it
in a table, as given below:

Table 14.1 is called an ungrouped frequency distribution table, or simply a frequency
distribution table. Note that you can use also tally marks in preparing these tables,
Q 3250678514

100 plants each were planted in 100 schools during Van Mahotsava. After one month, the number of plants that survived were recorded as :

Class 9 Chapter 14 Example 3
Solution:

To present such a large amount of data so that a reader can make sense of it easily,
we condense it into groups like 20-29, 30-39, . . ., 90-99 (since our data is from
23 to 98). These groupings are called ‘classes’ or ‘class-intervals’, and their size is
called the class-size or class width, which is 10 in this case. In each of these classes,
the least number is called the lower class limit and the greatest number is called the
upper class limit, e.g., in 20-29, 20 is the ‘lower class limit’ and 29 is the ‘upper class
limit’.

Also, recall that using tally marks, the data above can be condensed in tabular form as follows:

Presenting data in this form simplifies and condenses data and enables us to observe
certain important features at a glance. This is called a grouped frequency distribution
table. Here we can easily observe that 50% or more plants survived in 8 + 18 + 10 +
23 + 12 = 71 schools.

We observe that the classes in the table above are non-overlapping. Note that we
could have made more classes of shorter size, or fewer classes of larger size also. For
instance, the intervals could have been 22-26, 27-31, and so on. So, there is no hard
Q 3260678515

Let us now consider the following frequency distribution table which gives the weights of 38 students of a class:
Class 9 Chapter 14 Example 4
Solution:

Now, if two new students of weights 35.5 kg and 40.5 kg are admitted in this class,
then in which interval will we include them? We cannot add them in the ones ending
with 35 or 40, nor to the following ones. This is because there are gaps in between the
upper and lower limits of two consecutive classes. So, we need to divide the intervals
so that the upper and lower limits of consecutive intervals are the same. For this, we
find the difference between the upper limit of a class and the lower limit of its succeeding
class. We then add half of this difference to each of the upper limits and subtract the
same from each of the lower limits.
For example, consider the classes 31 - 35 and 36 - 40.
The lower limit of 36 - 40 = 36
The upper limit of 31 - 35 = 35
The difference = 36 – 35 = 1
So, half the difference = 1/2= 0.5

So the new class interval formed from 31 - 35 is (31 – 0.5) - (35 + 0.5), i.e., 30.5 - 35.5.
Similarly, the new class formed from the class 36 - 40 is (36 – 0.5) - (40 + 0.5), i.e.,
35.5 - 40.5.
Continuing in the same manner, the continuous classes formed are:
30.5-35.5, 35.5-40.5, 40.5-45.5, 45.5-50.5, 50.5-55.5, 55.5-60.5,
60.5 - 65.5, 65.5 - 70.5, 70.5 - 75.5.

Now it is possible for us to include the weights of the new students in these classes. But, another problem crops up because 35.5 appears in both the classes 30.5 - 35.5 and 35.5 - 40.5. In which class do you think this weight should be considered?
if it is considered in both classes, it will be counted twice. By convention, we consider 35.5 in the class 35.5 - 40.5 and not in 30.5 - 35.5.
Similarly, 40.5 is considered in 40.5 - 45.5 and not in 35.5 - 40.5.
So, the new weights 35.5 kg and 40.5 kg would be included in 35.5 - 40.5 and 40.5 - 45.5, respectively. Now, with these assumptions, the new frequency distribution table will be as shown below:

Now, let us move to the data collected by you in Activity 1. This time we ask you to present these as frequency distribution tables.

### Activity 2 :

Continuing with the same four groups, change your data to frequency tables.

Choose convenient classes with suitable class-sizes, keeping in mind the range of the data and the type of data.