Class 8 Maths Chapter 5 Notes - Data Handling

Graphical Representation

A graph is a diagram that represents data or values visually in an organised manner. When data are presented graphically it becomes easy to understand. The representation of data graphically can be done in various ways. Some of them are:

Pictograph: When the data are represented as pictures or symbols it is known as a pictograph.

Bar Graph: In a bar graph, the information is shown by bars of the same width with equal gaps, and the heights of the bars represent the respective values.

Double Bar Graph: To compare data, we use double bar graph as it shows information about two quantities simultaneously.

Organising and Grouping Data

Data that are available in an unorganised form are called raw data. To make this data meaningful, we have to arrange or group the data in a systematic manner. In tally marks, four vertical lines are drawn and for the fifth one, we draw a slanting line. The number of tallies after each value gives the frequency of that particular data.

The bar graph of a grouped frequency distribution or continuous class interval is called a histogram.
The class intervals are shown on the horizontal line and the frequencies of the class intervals are shown as the height of the bars. There is no gap between the bars as the classes are continuous.

The lower value of a class is called the lower-class limit. The higher value of a class is called the upper-class limit. The difference of the upper-class limit and the lower-class limit is called the class-size. This class-size gives the width of the bars of a histogram.

You may also need this
NCERT Solutions for class 8 Maths Chapter 5
NCERT Solutions for class 8 Maths Chapter 5 Exercise 5.1
NCERT Solutions for class 8 Maths Chapter 5 Exercise 5.2
NCERT Solutions for class 8 Maths Chapter 5 Exercise 5.3

Pie Chart

When data is represented in circular form, it is called a pie chart (or a circular chart). Each portion of a pie-chart shows a part of a whole. A pie chart is divided into various parts called sectors or slices. The minimum number of sectors that a pie chart can have is 2.

The sectors of a pie chart form a certain portion or percentage of the total pie-chart. The total angle formed at the centre of the chart is 360°.

The central angle for a particular component in a pie chart is value of component × 360° / Total value.

If the value of the components are expressed in percentages, the angle of the sector for a particular component is Percentage value of component × 360° / 100.
.
If the values of all the components are expressed as numbers, the percentage of a particular component is given as Percentage of Sector = Sector value × 100 / Total value.

Bigger the value of the sector, bigger is the sector value or vice versa.
If the sector angle for a component is given, the value of component is Sector angle × Total value / 360°.

If the percentage of each component is given, the value of component is Percentage of Sector × Total value / 100.

Steps to Construct a Pie Chart

• First, find the value of the angle of sector for each component using the formula given above.
• Second, draw a circle of any radius using a compass and draw a line from the centre to any point on the circle.
• Third, draw the angles you found for each sector using a protractor.
• Last, label the circular graph and label all its sectors.

Let us see an example of reading a pie chart.

The pie chart below shows the percentage of students in a school who like different fruits. The total number of students is 1000. How many students like banana?



We will find the value of each component using the formula
Value of component = Percentage of Sector × Total value / 100.
The total value of all the components = 1000
Here, we can see from the given pie chart that orange colour represents banana.
So, number of students who like banana = 24 × 1000 / 100
= 240

Hence, 240 students like banana in the school.

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Probability

Probability measures how likely an event can occur. It can range from 0 to 1, where 0 means the event is an impossible event, and 1 indicates that an event is a certain event.

The formula for probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes.

Probability of an event = Number of favourable outcomes/Total number of outcomes.

When some events have the same probability of occurrence, they are called equally likely events. When we throw a die, the probability of getting 2 is 1/6 and that of getting 3 is also 1/6. Hence, these events are equally likely events.

Complementary events occur when there are just two outcomes. One event occurs if and only if the other doesn't. The sum of probabilities of two complementary events is 1.

Let us see a real-life example where probability is used.

There are 55 students in a class, of whom 30 are girls, and the remaining are boys. If a student is selected randomly, what is the probability that the student chosen is a boy?

Answer:

The total number of students in the class = 55
Number of girls in the class = 30
Number of boys in the class = 55 – 30 = 25
Probability of choosing a boy

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