Course Content
Chapter 01 – Sets
A set is a group of elements in brackets that are related to one another. In this chapter, you will learn about the differences and similarities between an equal set and an equivalent set, and describe the notion and types of sets.
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Chapter 03 – Factors and Multiples
Multiples and factors are basic mathematical concepts. Review these terms and how they are applied to real-world scenarios, and practice applying them to solve sample word problems. Learning how to divide can be a little challenging, but knowing some basic rules about dividing can help. In this chapter, you'll learn about the divisibility rules that apply to numbers.
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Chapter 04 – Integers
An integer is a whole number (not a fractional number) that can be positive, negative, or zero. In this chapter, we'll learn about mathematical operations with integers using the operations of addition, subtraction, multiplication, and division. Discover the properties of integers and how those properties affect the solution to different types of math problems.
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Chapter 05 – Simplification
Simplifying math expression is an important part of helping students learn how to work and think algebraically. The order of operations in mathematics is the sequence in which a problem is solved. In this chapter, we'll explore the definition and examples of the order of operations in math, discover the steps involved, and learn the shortcut for remembering the steps defined by the acronym BODMAS and PEMDAS.
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Chapter 06 – Ratio and Proportions
Ratios allow us a way to mathematically compare two or more items, and proportions can help us find out even more information. In this chapter, we'll learn the definition of ratios and proportions, and understand how to calculate the ratio and proportion problems.
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Chapter 07 – Financial Arithmetic
Many values we come across regularly change frequently. In this chapter, we will look at examples when a quantity decreases in value, and how such decreases can be represented using percentages. A company may have a great product but if they are losing money, it will eventually go out of business. We will explore profit and loss from an economic perspective.
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Chapter 08 – Introduction to Algebra
To evaluate simple algebraic expressions, substitute a number for each variable and solve. In this chapter, we'll learn the steps for evaluating simple algebraic expressions, including rules for order of operations and parentheses, and tackle the practice problems.
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Chapter 10 – Geometry
Geometry is a sector of mathematics that analyzes shapes, lines, and surfaces. It is possible to construct different geometric shapes and patterns using lines and angles. In this chapter, we'll explore the definition of the basics of geometry: points, lines, and angles, geometric construction, the tools required for the job, and how to copy angles and line segments.
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Chapter 11 – Perimeter and Area
A perimeter is a measurement used to determine the distance of a path around the outer edge of a two-dimensional object. In this chapter, we'll discover the formula to calculate perimeter for various shapes and consider the usefulness of these equations through examples. Discover how to find the area of an irregular polygon. Explore formulas for the area of regular polygons, learn how to divide an irregular polygon into a series of regular polygons, and see how to find the area using those pieces.
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Chapter 12 – Three Dimensional Shapes
Geometric measurements can be taken for one-, two-, and three-dimensional shapes. In this chapter, we'll explore the most common formulas one would use to find the perimeter, area, surface area, and volume of three-dimensional figures.
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Chapter 13 – Information Handling
Data handling refers to the process of gathering, recording, and presenting information in a way that is helpful to others - for instance, in graphs or charts.
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Mathematics – VI
About Lesson

What is Data?

Data can be defined as a systematic record of a particular quantity. It is the different values of that quantity represented together in a set. It is a collection of facts and figures to be used for a specific purpose such as a survey or analysis. When arranged in an organized form, it can be called information.

 

What are grouped data and ungrouped data?

 

Grouped data means the data (or information) given in the form of class intervals such as 0-20, 20-40, and so on. Ungrouped data is defined as the data given as individual points (i.e. values or numbers) such as 15, 63, 34, 20, 25, and so on.

 

What is a grouped data example?

 

Suppose we have data ranges from 0 to 50 like 2, 17, 0, 1, 8, 19, 43, 2, 1, 32, and so on. In this case, we can group the data into classes such as 0-10, 10-20,…,40-50. This is a simple example of grouped data.

 

What are the advantages of grouping data?

 

The main advantages of grouping data are:

  • Assist us in concentrating on essential subgroups mainly and overlooks trivial ones.
  • Helps in increasing the efficiency and correctness of the required estimation.

 

How do you group data into a class?

 

An important technique used for grouping the given data is tally marks. With the help of a tally marks table, it is possible to convert the data into classes without any confusion. Then find the height (or size) of the class interval by dividing the difference between the highest and the least data value by the number of classes we want (in the case of the decimal value, the nearest whole number defines the class size).

 

How many classes can a grouped data have?

 

For ideal grouped data, it is suggested to have the number of class intervals as a minimum of 5 and a maximum of 20. But we can also observe grouped data with less than 5 class intervals in many situations.

 

Types of Data

 

Data may be qualitative or quantitative. 

 

Qualitative Data:

They represent some characteristics or attributes. They depict descriptions that may be observed but cannot be computed or calculated.

 

For example, data on traits such as intelligence, honesty, wisdom, cleanliness, and creativity collected using the students of your class sample would be classified as qualitative. They are more exploratory than conclusive in nature.

 

Quantitative Data: 

These can be measured and not simply observed. They can be numerically represented and calculations can be performed on them.

 

For example, data on the number of students playing different sports from your class estimate how many of the total students play which sport. This information is numerical and can be classified as quantitative.

 

Data Collection

 

Depending on the source, it can classify as primary data or secondary data. Let us take a look at them both.

 

Primary Data

These are the data that are collected for the first time by an investigator for a specific purpose. Primary data are ‘pure’ in the sense that no statistical operations have been performed on them and they are original. An example of primary data is the Census of Pakistan.

 

Secondary Data

They are the data that are sourced from someplace that has originally collected it. This means that this kind of data has already been collected by some researchers or investigators in the past and is available either in published or unpublished form. This information is impure as statistical operations may have been performed on them already.

Exercise Files
Qualitative and Quantitative Observations.pdf
Size: 331.58 KB
Quantitative and Qualitative variables.pdf
Size: 127.96 KB
Quantitative vs Qualitative.pdf
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