RS Aggarwal Class 8 Mathematics Solutions Chapter-21 Data Handling

We have provided step by step solutions for all exercise questions given in the pdf of Class 8 RS Aggarwal Chapter-21 Data Handling. All the Exercise questions with solutions in Chapter-21 Data Handling are given below: 

Exercise (Ex 21A) 21.1

Exercise (Ex 21B) 21.2

Exercise (Ex 21C) 21.3

Data Handling - At A Glance

Data handling is an important chapter of class 8 mathematics as it forms a base for future complex chapters like statistics and probability. It is very essential for class 8 students to study these chapters well. Some of the important concepts discussed in the chapter are:

• An unorganized form of data is known as raw data.

• We should always organize data systematically in order to draw meaningful inferences from the data.

• Frequency refers to the number of times a specific entry appears.

• Raw data are grouped together systematically in the form of grouped frequency distribution.

• Grouped data are represented using the histogram.

• Histograms are a type of bar diagram where the horizontal axis is class intervals and bars represent the frequency of the class interval. 

• Pie charts can also be used to represent data.

• The other name for pie charts is circle graphs.

• Those experiments whose outcomes cannot be predicted in advance are known as random experiments.

• When each outcome in an experiment has an equal chance of occurring then such outcomes are known as equally likely outcomes.

• The probability of an experiment is calculated as the number of outcomes of an event divided by the total number of outcomes of the experiment.

• More than one outcome of an experiment makes an event.

• Concepts of probability and chances are related to real life.

What is Data?  

The information or facts that are gathered with the help of observations and measurements is known as data.  

The actual meaning of data can only be explained with the help of suitable examples:-

Suppose your class teacher takes a physics unit test for the whole class. She distributes the result the next day, and you find out that you have got 8/10. Similarly, your best friend got an 8.5/10. Likewise, the entire class got some marks. The marks that you and your classmates got is known as Data. 

In mathematics, we deal with quantitative data, i.e. the data that can be expressed as numbers. The marks that you and your classmates got are the example of quantitative data. 

Another example of data is:-

Suppose your PT teacher measures the weight of each student in the class. Your weight is 50kgs. Your friend’s weight is 49.5 kgs. Likewise, each student has a particular weight. The value of the weight, such as 50,49.5 and so on, are known as data.

Data is of two types: raw data and grouped data.

1. Raw Data: When the data is collected it is not arranged in a systematic manner and is presented randomly. Such data is known as raw data.

2. Grouped Data: When the raw data collected is further classified into groups in a systematic manner then that data is known as grouped data.

What is Data Handling?

Data Handling refers to the systematic organisation of data. It involves collecting, recording, analysing, and presenting data that aids in understanding and drawing inferences from the data collected. 

Data is generally collected in an unorganised form. This unorganised form of information is known as raw data. Systematic organization of raw data is done in data handling.

For example:-

Suppose, 15 students are asked about choosing their favourite ice cream flavour from chocolate, strawberry, vanilla and other flavours. The response of the students are as follows:-

Strawberry, vanilla, other flavours, vanilla, chocolate, chocolate, vanilla, strawberry, different flavours, vanilla, strawberry, chocolate, vanilla, other flavours, strawberry.

The above data is in the form of raw data. This data needs an organisation to find out the favour that is liked the most.

The tally marks of each flavour represent the no. of students that like a particular flavour. It is known as the frequency of the flavour. The above table is known as the frequency distribution table.

What is Frequency? 

Frequency can be defined as the number of times an observation occurs during a study. In the above example, strawberry ice cream is liked by three students; hence the frequency of strawberry ice cream is 4. Likewise, the frequency of Vanilla, chocolate and other ice cream is 5, 3, 3, respectively. 

When we represent the frequency of the data in the form of a table, then that table is known as the frequency distribution table.

What is Grouped Frequency Distribution?

A grouped frequency distribution is required when the number of data is large. For example, a frequency distribution table of marks obtained by 30 students in a mathematics test has to be made, and they are given in the form of raw data. The total marks of the test are 20.

17, 8, 9, 4, 9, 6, 7, 9, 18, 8, 19, 19, 17, 16, 15, 18, 11, 4, 18, 9, 7, 15, 15, 14, 18, 14, 19, 15, 16, 8

The groups 0-10 and 10- 20 are called class intervals, and the distribution is known as grouped frequency distribution. In group 0-10, 0 is known as the lower class limit, and 10 is known as the upper-class limit. Similarly, in the next group, 10-20, 10 is known as the lower class limit, and 20 is known as the upper-class limit. A histogram represents a grouped frequency distribution. 

The difference between the upper-class limit and the lower class limit gives us the class interval’s width or size. The width of each class interval in the above example is 10.

What is the Class Interval?

Class interval is the range of each group in which the raw data is grouped. For example, 1 -10, 11-20, 21-30 are examples of class intervals.

What are Pictographs?

Representation of data by the use of appropriate pictures is known as a pictograph. Each picture or symbol that is used in data presentation represents a certain value.

What are Bar Graphs and Double Bar Graphs?

Bar graphs are pictorial graphs that represent data in the form of bars that have uniform width but whose height varies on the basis of the value of the respective data.

Simultaneous representation of two sets of data in a bar graph is known as a double bar graph. This type of graph is used for the comparison of the data.

Did you know?

Herman Hollerith (1860 - 1929) was a statistician who invented the tabulating machine that helped in data handling to save a significant amount of time while calculating census.