Data Handling and Presentation Chapter Notes | Mathematics (Maths) Class 6 PDF Download

Introduction

In our daily lives, we often come across various pieces of information, whether it's the list of our classmates' favorite colors or the measurements of different students' weights. This collection of information is what we call data. 

Data is essentially any set of facts, numbers, observations, or measurements that help us understand and convey details about the world around us.

In today's world, we are surrounded by data in many forms—charts, graphs, tables, and more. These visual representations help us make sense of the information, allowing us to draw conclusions and make decisions based on it. Understanding how to present and interpret data correctly is an important skill. In this chapter, we will delve into the different ways data is displayed and learn how to analyze it effectively to make accurate inferences.

Collecting and Organizing Data

Imagine you and your friends are at a school event where there are several fun activities, like a magic show, a dance-off, and a treasure hunt. You want to find out which activity is the most popular. So, you ask each of your friends which activity they liked the most and note down their answers. This list of activities is data.

But just having this list doesn't immediately tell you which activity is the most popular. To figure that out, you need to organize the data.

For example: Let’s say you have the following preferences:

• Magic Show: 7 friends
• Dance-Off: 5 friends
• Treasure Hunt: 8 friends

To make things clearer, you could use tally marks. For each friend who liked a particular activity, you put a tally mark. When you reach five marks, you cross the four with a line like this:  for easier counting.

This way, it’s easy to see that the Treasure Hunt is the most popular activity because it has the most tally marks.

Tally marks are a quick way to count things in groups of five. You draw a vertical line for each count, and when you reach five, you cross the four vertical lines with a diagonal line to make it easy to see groups of five.

Now, imagine another situation. Your teacher, Mrs. Sandhya, asks everyone in class about their shoe sizes. She writes down all the numbers on the board, like this:

• 4, 5, 3, 4, 3, 4, 5, 5, 4
• 5, 5, 4, 5, 6, 4, 3, 5, 6
• 4, 6, 4, 5, 7, 5, 6, 4, 5

At first glance, this list looks a bit jumbled. To make it easier to see which shoe sizes are most common, she decides to arrange the data in ascending order. 
This means she puts the numbers in order from smallest to largest:

• 3, 3, 3
• 4, 4, 4, 4, 4, 4, 4
• 5, 5, 5, 5, 5, 5, 5, 5
• 6, 6, 6, 6
• 7

By arranging the numbers this way, it becomes much easier to see which shoe sizes are the most common. In this case, size 5 is the most popular because it appears the most frequently.

This method of organizing data—whether by using tally marks to count preferences or by arranging numbers in order—helps you make sense of the information quickly and easily.

Pictographs

A pictograph is a fun and simple way to show data using pictures instead of numbers. Imagine you're at a school event, and you want to know how many students took part in different activities like drawing, singing, or dancing. Instead of writing down numbers, you decide to draw pictures.

For example:

You could draw these pictures in a chart to represent how many students took part in each activity: 

With just a quick glance at this pictograph, you can tell which activity was the most popular and which was the least popular.

A pictograph represents data through pictures of objects. It helps answer questions about data with just a quick glance.

Example: Favorite Snacks in Class
Let’s say your teacher asked everyone about their favorite snack and made a pictograph to show the results. Each picture of a snack represents one student:

Now, let’s answer some questions based on this pictograph:

1. How many students like cookies?

   • There are 7 cookie pictures, so 7 students like cookies.

2. How many students like fruit?

   • There are 3 fruit pictures, so 3 students like fruit.

3. Which snack is the least popular?

   • Candy is the least popular because there is only 1 candy picture, meaning only 1 student likes candy.

This pictograph makes it super easy to see which snacks are the favorites in your class, just by looking at the pictures!

Drawing a Pictograph

Example 1: One day, let’s say you wanted to track how many hours you spent playing different games each week. Here’s the data you collected:You decide to create a pictograph to present this data. You choose to use one symbol to represent one hour of gameplay. Your pictograph would look like this:

This pictograph makes it easy to see how much time you spent playing games each day.

Example 2: Now, imagine your friend wants to track how many books she read each month. Here’s her data:

Your friend realizes that using one symbol to represent each book might make her pictograph too crowded and difficult to read. Instead, she decides to use one symbol to represent 5 books. Her pictograph would look like this:

This method makes it easier to see the data without using too many symbols, saving both time and space.

But let's say another friend, Gina, also wants to show how many books she read over the summer. Here’s her data:

Gina decides to use one symbol to represent 5 books. Here’s her pictograph:

In this case, representing 33 books with the chosen scale is tricky because 33 is not an exact multiple of 5. To deal with this, Gina uses six symbols for 30 books and a half symbol to represent the remaining 3 books.

Challenges in Preparing a Pictograph

• Pictographs are a fun and easy way to show data using pictures. Instead of just numbers, they use pictures or symbols to represent information.
• Pictographs make it easy to answer questions and understand data quickly. For example, by looking at a pictograph, you can easily see which game is the most popular, which color is liked the most, how many students are absent, and so on.
• In a pictograph, you can arrange the categories either across (horizontally) or down (vertically). For each category, you draw simple pictures or symbols in the rows or columns based on how many times that category appears.
• A scale or key is also included in a pictograph to explain what each picture or symbol stands for. For example, one picture might represent 1 student or even 5 students. This helps you understand the data better.
• However, it can be tricky to make a pictograph when there is a lot of data or when the numbers don't exactly match the scale or key.

Bar Graphs

Bar graphs are similar to pictographs in that they help us quickly understand and compare information, like identifying the highest value or comparing different categories. However, when there's a lot of data, using pictographs can become difficult and take a lot of time.

In bar graphs, we draw bars of the same width either horizontally or vertically, with equal spaces between them. The length or height of each bar shows the value or number it represents. Just like in pictographs, when the numbers are large, we can use a scale or key to make it easier to read the graph.

Example: Imagine you and your friends are tracking how many books each of you read over the summer. Here's the data you collected:

You decide to create a bar graph to show this data. In the graph, each bar’s height represents the number of books read by each friend. Here’s how it would look:

In this bar graph, the length or height of each bar shows the number of books read. The taller the bar, the more books that friend read. It’s an easy way to compare at a glance who read the most and who read the least.

A bar graph is a visual tool that uses bars to represent data, allowing for easy comparison of different categories.

Key Points to Remember:

• Bar graphs help you compare different categories easily.
• The length or height of each bar represents the value for that category.
• Sometimes, using a scale (like 1 unit = 10 people) makes it easier to represent large numbers.
• Bar graphs are useful when you have a lot of data or when you want to see trends over time.

Drawing a Bar Graph

Imagine you want to track how many hours you and your friends spend playing different sports in a week. Here’s the data you collected:

To represent this data using a bar graph, follow these steps:

1. Draw Axes: First, draw a horizontal line (x-axis) and a vertical line (y-axis). On the horizontal line, you’ll list the names of the sports, equally spaced. On the vertical line, you’ll write the numbers representing the hours spent on each sport.
2. Choose a Scale: Decide how many hours will be represented by one unit length on the vertical line. If each unit represents 1 hour, it should fit nicely on your paper. In this case, 1 unit length will equal 1 hour.
3. Draw the Bars: For soccer, you’ll draw a bar that’s 8 units high (since you spent 8 hours playing soccer). Similarly, draw bars for basketball, tennis, and swimming according to their respective hours.

Why Bar Graphs Are Useful

• Bar graphs, like pictographs, are a great way to show data visually. They use bars that are equally spaced and of the same width, where the length or height of each bar represents how often something happens or how much there is of something.
• Each bar stands for a different category, and the height or length of the bar shows the amount or frequency for that category (for example, how much something costs or how many runs were scored).
• The bars are spaced evenly to show that they are separate and represent equal categories. Bar graphs make it easier to understand and compare information quickly, even faster than looking at a list of numbers.
• When making a bar graph, you need to choose a scale, which tells you what each unit of length on the graph stands for (like 1 unit = 1 student or 1 unit = 200 people). The scale should be chosen based on the smallest and largest numbers in your data so that the graph looks neat and fits well on the paper or poster. The scale should always start from zero.

Artistic and Aesthetic Considerations

When you're creating a visual presentation of data, like a pictograph or a bar graph, there are some artistic and aesthetic aspects you can think about to make your presentation more interesting and effective. Besides following the basic steps, like choosing an appropriate scale to fit the graph into your space, it’s also important to make the graph visually appealing and easy to understand. This way, your audience can quickly grasp the information you're sharing.

Example: Tallest Mountains on Each Continent
Imagine you have a list of the tallest mountains on each continent and their heights:

You might want to know how much taller Mount Everest is compared to Mount Koscuiszko, or whether Denali and Kilimanjaro have similar heights. Looking at just the numbers in a table can make this a bit tricky.

Using a Bar Graph

To make this easier to understand, you could convert the table of numbers into a bar graph. Imagine drawing horizontal bars, where each bar’s length represents the height of a mountain. This way, you can quickly compare the heights of all these mountains.

But here’s a tip: since we’re talking about the heights of mountains, it might be more visually appealing to rotate the bars so they grow upwards, like mountains themselves! This type of bar graph, where the bars grow vertically, is called a column graph.

Why Vertical Bars?

Vertical bars (columns) are more intuitive for representing things like height because they naturally grow upwards, just like the mountains or tall buildings they represent. On the other hand, if you were showing something like the distance between two cities, you might prefer horizontal bars, which stretch out in a line, just like the roads connecting those cities.

Infographics

When you take data visualizations like bar graphs and make them even more visually appealing by adding artistic touches, you create something called infographics. Infographics use eye-catching visuals to communicate information more clearly and quickly, making the data both informative and engaging.

Understanding Infographics with examples
Example 1: Imagine you and your friends are comparing how many apples, bananas, and oranges each of you ate last week. You could make a simple bar graph to show the numbers:

In a bar graph, each bar would represent how many of each fruit was eaten, and the height of the bar would show the number. For example:

• Apples: A bar 5 units high
• Bananas: A bar 3 units high
• Oranges: A bar 4 units high

Turning It into an Infographic
Now, let’s say you want to make this data look more fun and interesting. Instead of using plain bars, you decide to draw pictures of the fruits:

• You draw 5 apples stacked on top of each other to show how many apples were eaten.
• You draw 3 bananas in a row to represent the bananas.
• You draw 4 oranges next to each other for the oranges.

This is what we call an infographic—it’s a way of showing data using pictures instead of just bars. It makes the information easier to understand and more fun to look at.

Example 2: Tallest Mountains
Let’s say we have the data about the tallest mountains on each continent. Initially, we used a bar graph with vertical bars to represent the heights of these mountains:

In the bar graph, each bar was the same width, and the height of the bar represented the height of the mountain.

Turning a Bar Graph into an Infographic
Now, if we wanted to turn this bar graph into an infographic, we could make the bars look like mountains by changing the shape of the bars from rectangles to triangles. We might also add some color to make the infographic more visually appealing.

For example, each triangle could represent a mountain, with the height of the triangle showing how tall the mountain is. Here’s how it might look:

• Everest: A tall, sharp triangle reaching up to 8848 meters
• Aconcagua: A slightly shorter triangle at 6962 meters
• Kilimanjaro: A medium triangle at 5895 meters
• Koscuiszko: A small triangle at 2228 meters

This infographic would be more visually striking, and it might catch your attention more quickly than a plain bar graph. However, there are some things to be cautious about.

Potential Pitfalls of Infographics

In this infographic, the taller triangles (mountains) might also appear wider. This could unintentionally suggest that taller mountains are also wider, which isn’t necessarily true. For example, Mount Everest is the tallest, but that doesn’t mean it’s the widest. This visual choice could be misleading, implying information that the data doesn’t actually support.

Making Infographics Even More Engaging

• Let’s take it a step further. Imagine creating an infographic where all these mountains are part of an imaginary mountain range. You could add details like snowcaps, trees, or climbers to make it look even more realistic. 
• This would definitely make the infographic more engaging and fun to look at.
• However, there’s a catch. In this realistic mountain range, Everest might look twice as tall as Elbrus. 
• But if you do the math, you’ll see that 5642 meters (the height of Elbrus) times two is 11,284 meters, which is way taller than Everest’s actual height of 8848 meters! So, while the infographic looks cool, it might give a misleading impression of the data.

Be Careful with Infographics
Infographics are a powerful tool for presenting data in a visually appealing way, but you have to be careful. While it’s great to make your data look interesting, you don’t want to accidentally mislead people by suggesting something that isn’t true. Always double-check that your visuals accurately represent the data and that they don’t add unintended meanings.

Why This Matters
While making your data look interesting, you want to make sure you’re still showing the truth. If you make one type of fruit look much bigger than the others just because of the way you drew it, you might accidentally make people think you ate more of that fruit than you actually did.

Key Points

• Collecting favorite items, like ice cream flavors, creates a list, which is data.
• Data is information collected as facts, numbers, or descriptions.
• Tally marks and ordering help organize data to identify popular choices quickly.
• Pictographs use pictures to represent data; each picture can stand for one or more items.
• Bar graphs use bars to compare data; the height or length shows the value.
• Bar graphs are helpful for large data or precise comparisons, like population over years.
• Infographics make data visually appealing but must accurately represent information to avoid misleading viewers.