Data Handling

This chapter focuses on the topic of data handling and emphasizes the use of visual aids such as pictures, bars and line graphs to enhance our ability to understand numerical information. This approach not only simplifies the process of learning about numbers and information but also adds an element of enjoyment and interest to it.

Data Handling

Data is often conveyed through visual means such as tables, images, bars and diagrams. Data handling utilizes visual representations like images, bars or figures to enhance students' understanding of numerical data.

Data handling serves as the collection of raw information which forms the basis from which statistics are derived. Statistics represent the outcomes of data which includes the processes of interpretation and presentation.

Statistics: Making Sense of Numbers

Statistics is a special branch of mathematics that deals with the interpretation, gathering, organization and presentation of data.

Terms related to statistics

Range:

→ Range refers to the spread of data. It is the difference between the highest and lowest observations.
→ Formula: Range = Maximum observation - Minimum observation

Mode:

→ Mode represents the number that appears most frequently.
→ To find the mode, arrange data in ascending order and count the frequency of each number. Hence, the mode is the observation with the highest frequency.
→ Formula: Mode = Most Frequently Occurring observation

Mean:

→ The mean is the average of a set of numbers which is obtained by summing all the values and dividing by the total count.
→ Formula:

Various types of graphical representations

Various types of graphical representations exist for this purpose as follows:

1. Pictographs
2. Bar graphs
3. Pie charts
4. Line graphs

These graphical tools facilitate a clearer understanding of numerical information.

Pictograph

A pictograph is a visual representation for illustrating data through the use of images. Each image within a pictograph symbolizes specific information. It conveys data frequencies by employing images or symbols that relate to the data. Pictographs are methods for presenting statistical information.

Example: The given pictograph shows the number of gas cylinders sold by a vendor in five days.

What is the total number of gas cylinders sold by a vendor in all five days?

a) 125
b) 175
c) 225
d) 275

Answer: b) 175

Explanation: Total number of gas cylinders sold by a vendor in all five days
= 7 × (6 + 4 + 7 + 3 + 5)
= 7 × 25
= 175

Pie chart

A pie chart is a type of graph that represents the data in a circular graph.

Example: The pie chart shows the marks obtained by a student in an examination in the decimal number system. What are the marks scored in mathematics if the student secures 1080 marks in all subjects?

a) 338 marks
b) 358 marks
c) 378 marks
d) 398 marks

Answer: c) 378 marks

Explanation: Marks secured in mathematics
= Decimal number × Total score secured in mathematics
= 0.35× 1080
= 378 marks

Bar graph

A bar graph is a visual representation of data, quantities or numerical values using bars (or rectangles). Its primary purpose is to facilitate the comparison of various data types.  It is also called a column graph.

Example: The bar graph given below shows the marks scored by students of a class.

What is the number of students who scored more than 73 marks?

a) 25
b) 50
c) 75
d) 85

Answer: c) 75

Explanation: Number of students who scored more than 71 marks
= 5 + 20 + 5 + 5 + 15 + 25 = 75

Line graph

A line graph is a visual representation of data that illustrates the connection between various points through a continuous line which shows the relationship between these points. It is constructed by connecting data points with line segments. It is also called a line chart or a line plot.

Example: The given line graph shows the number of magazines students have.

What is the fraction of the number of magazines Lee had to the number of magazines Evola had?  

a) 3/5
b) 5/3
c) 5/6
d) 6/5

Answer: c) 5/6

Explanation: Fraction of the number of magazines Lee had to the number of magazines Evola had = 25/30
                                                                                                                                                 = 5/6