Class 6 Maths Chapter 4 Notes Data Handling and Presentation
Class 6 Maths Notes Chapter 4 – Class 6 Data Handling and Presentation Notes
→ Facts, numbers, measures, observations, and other descriptions of things that convey information about those things are called data.
→ Data can be organized in a tabular form using tally marks for easy analysis and interpretation.
→ Frequencies are the counts of the occurrences of values, measures, or observations.
→ Pictographs represent data in the form of pictures/objects or parts of objects. Each picture represents a frequency that can be 1 or more
than 1 – this is called the scale, and it must be specified.
→ Bar graphs have bars of uniform width; the length or height then indicates the total frequency of occurrence. The scale that is used to convert length/height to frequency must again be specified.
→ Choosing the appropriate scale for a pictograph or bar graph is important to accurately and effectively convey the desired information/data and to also make it visually appealing.
→ Other aspects of a graph also contribute to its effectiveness and visual appeal, such as how colours are used, what accompanying pictures are drawn, and whether the bars are horizontal or vertical. These aspects correspond to the artistic and aesthetic side of data handling and presentation.
→ However, making visual representations of data too “fancy” can also sometimes be misleading.
→ By reading pictographs and bar graphs accurately, we can quickly understand and make inferences about the data presented.
If you ask your classmates about their favourite colours, you will get a list of colours. This list is an example of data. Similarly, if you measure the weight of each student in your class, you would get a collection of measures of weight—again data. Any collection of facts, numbers, measures, observations, or other descriptions of things that convey information about those things is called data.
We live in an age of information. We constantly see large amounts of data presented to us in new and interesting ways. In this chapter, we will explore some of the ways that data is presented, and how we can use some of those ways to correctly display, interpret, and make inferences from such data!
Collecting and Organising Data Class 6 Notes
Navya and Naresh are discussing their favourite games.
Naresh and Navya decided to go to each student in the class and ask what their favourite game was. Then they prepared a list. Navya is showing the list:
She says (happily), “I have collected the data. I can figure out the most popular game now!” A few other children are looking at the list and wondering, “We can’t yet see the most popular game. How can we get it from this list?”
Shri Nilesh is a teacher. He decided to bring sweets to the class to celebrate the new year. The sweets shop nearby has jalebi, gulab jamun, gujiya, barfi, and rasgulla. He wanted to know the choices of the children. He wrote the names of the sweets on the board and asked each child to tell him their preference. He put a tally mark ‘|’ for each student and when the count reached 5, he put a line through the previous four and marked it as .
Shri Nilesh requested one of the staff members to bring the sweets as given on the table. The above table helped him to purchase the correct number of sweets. To organize the data, we can write the name of each sweet in one column and using tally signs, note the number of students who prefer that sweet. The numbers 6, 9, and… are the frequencies of the sweet preferences for jalebi, and gulab jamun … respectively. Sushri Sandhya asked her students about the sizes of the shoes they wear. She noted the data on the board.
She then arranged the shoe sizes of the students in ascending order:
3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7
Pictographs Class 6 Notes
Pictographs are one visual and suggestive way to represent data without writing any numbers. Look at this picture — you may be familiar with it from previous classes.
This picture helps you understand at a glance the different modes of travel used by students. Based on this picture, answer the following questions:
- Which mode of travel is used by the most number of students?
- Which mode of travel is used by the least number of students?
A pictograph represents data through pictures of objects. It helps answer questions about data with just a glance. In the above pictograph, one unit or symbol ( ) is used to represent one student. There are also other pictographs where one unit or symbol stands for many people or objects.
Example: Nand Kishor collected responses from the children of his middle school in Berasia regarding how often they slept at least 9 hours during the night. He prepared a pictograph from the data:
Answer the following questions using the pictograph:
- What is the number of children who always slept at least 9 hours at night?
- How many children sometimes sleep at least 9 hours at night?
- How many children always slept less than 9 hours each night? Explain how you got your answer.
Solutions
- In the table, there are 5 pictures for ‘Always’. Each picture represents 10 children. Therefore, 5 pictures indicate 5 × 10 = 50 children.
- There are 2 complete pictures (2 × 10 = 20) and a half picture (half of 10 = 5). Therefore, the number of children who sleep at least 9 hours only sometimes is 20 + 5 = 25.
- There are 4 complete pictures for ‘Never’. Hence 4 × 10 = 40 children never sleep at least 9 hours in a night, i.e., they always sleep less than 9 hours.
Drawing a Pictograph
One day, Lakhanpal collected data on how many students were absent in each class.
He created a pictograph to present this data and decided to show 1 student as in the pictograph.
Meanwhile, his friends Jarina and Sangita collected data on how many students were present in each class.
If they want to show their data through a pictograph, where they also use one symbol for each student, as Lakhanpal did, what are the challenges they might face?
Jarina made a plan to address this since there were many students, and she decided to use to represent 5 students. She figured that would save time and space too.
Sangita decided to use one to represent 10 students instead. Since she used one to show 10 students, she had a problem showing 25 students and 35 students in the pictograph. Then, she realized she could use to show 5 students.
- Pictographs are a nice visual and suggestive way to represent data. They represent data through pictures of objects.
- Pictographs can help answer questions and make inferences about data with just a glance (in the examples above— about favorite games, favorite colours, most common modes of conveyance, number of students absent, etc.).
- By reading a pictograph, we can quickly understand the frequencies of the different categories (for example, cricket, hockey, etc.), and the comparisons of these frequencies.
- In a pictograph, the categories can be arranged horizontally or vertically. For each category, simple pictures and symbols are then drawn in the designated columns or rows according to the frequency of that category.
- A scale or key (for example, : 1 student or : 5 students) is added to show what each symbol or picture represents. Each symbol or picture can represent one unit or multiple units.
- It can be more challenging to prepare a pictograph when the amount of data is large or when the frequencies are not exact multiples of the scale or key.
Bar Graphs Class 6 Notes
Have you seen graphs like this on TV or in a newspaper?
Like pictographs, bar graphs can help us to quickly understand and interpret information, such as the highest value, the comparison of values of different categories, etc. However, when the amount of data is large, presenting it by a pictograph is not only time-consuming but at times difficult too. Let us see how data can be presented instead of using a bar graph.
Let’s take the data collected by Lakhanpal earlier, regarding the number of students absent on one day in each class.
He presented the same data using a bar graph.
When making bar graphs, bars of uniform width can be drawn horizontally or vertically with equal spacing between them; then the length or height of each bar represents the given number. As we saw in pictographs, we can use a scale or key when the frequencies are larger. Let us look at an example of vehicular traffic at a busy road crossing in Delhi, which was studied by the traffic police on a particular day. The number of vehicles passing through the crossing each hour from 6 am to 12:00 noon is shown in the bar graph. One unit of length stands for 100 vehicles.
We can see that the maximum traffic at the crossing is shown by the longest bar, i.e., for the time interval 7-8 a.m. The bar graph shows that 1200 vehicles passed through the crossing at that time. The second longest bar is for 8-9 a.m. During that time, 1000 vehicles passed through the crossing. Similarly, the minimum traffic is shown by the smallest bar, i.e., the bar for the time interval 6-7 a.m. During that time, only about 150 vehicles passed through the crossing. The second smallest bar is that for the time interval 11 a.m.-12 noon when about 600 vehicles passed through the crossing. The total number of cars passing through the crossing during the two-hour interval 8.00-10.00 am as shown by the bar graph is about 1000 + 800 = 1800 vehicles.
Example:
This bar graph shows the population of India in each decade over 50 years. The numbers are expressed in crores. If you were to take 1 unit length to represent one person, drawing the bars would be difficult! Therefore, we chose the scale so that 1 unit represents 10 crores. The bar graph for this choice is shown in the figure. So a bar of length 5 units represents 50 crores and of 8 units represents 80 crores.
- Based on this bar graph, what may be a few questions you may ask your friends?
- How much did the population of India increase over 50 years?
- How much did the population increase in each decade?
Drawing a Bar Graph Class 6 Notes
In a previous example, Shri Nilesh prepared a frequency table representing the sweet preferences of the students in his class. Let’s try to prepare a bar graph to present his data.
1. First, we draw a horizontal line and a vertical line. On the horizontal line, we will write the name of each of the sweets, equally spaced, from which the bars will rise by their frequencies; and on the vertical line, we will write the frequencies representing the number of students.
2. We must choose a scale. That means we must decide how many students will be represented by a unit length of a bar so that it fits nicely on our paper. Here, we will take 1 unit length to represent 1 student.
3. For Jalebi, we therefore need to draw a bar having a height of 6 units (which is the frequency of the sweet Jalebi), and similarly for the other sweets we have to draw bars as high as their frequencies.
4. We therefore get a bar graph as shown below.
When the frequencies are larger and we cannot use the scale of 1 unit length = 1 number (frequency), we need to choose a different scale as we did in the case of pictographs.
Example: The number of runs scored by Smriti in each of the 8 matches is given in the table below:
In this example, the minimum score is 0 and the maximum score is 100. Using a scale of 1 unit length = 1 run would mean that we have to go all the way from 0 to 100 runs in steps of 1. This would be unnecessarily tedious. Instead, let us use a scale where 1 unit length = 10 runs. We mark this scale on the vertical line and draw the bars according to the scores in each match. We get the following bar graph representing the above data.
Example: The following table shows the monthly expenditure of Imran’s family on various items:
To represent this data in the form of a bar graph, here are the steps:
- Draw two perpendicular lines, one horizontal and one vertical.
- Along the horizontal line, mark the ‘Items’ with equal spacing between them, and along the vertical line, mark the corresponding expenditures.
- Take bars of the same width, keeping a uniform gap between them.
- Choose a suitable scale along the vertical line. Let 1 unit length = ₹ 200, and then mark and write the corresponding values (₹ 200, ₹ 400, etc.) representing each unit length.
Finally, calculate the heights of the bars for various items as shown below.
Here is the bar graph that we obtain based on the above steps:
- Like pictographs, bar graphs give a nice visual way to represent data. They represent data through equally spaced bars, each of equal width, where the lengths or heights give frequencies of the different categories.
- Each category is represented by a bar where the length or height depicts the corresponding frequency (for example, cost) or quantity (for example, runs).
- The bars have uniform spaces between them to indicate that they are free-standing and represent equal categories.
- The bars help in interpreting data much faster than a frequency table. By reading a bar graph, we can compare frequencies of different categories at a glance.
- We must decide the scale (for example, 1 unit length = 1 student or 1 unit length = ₹ 200) for a bar graph based on the data, including the minimum and maximum frequencies so that the resulting bar graph fits nicely and looks visually appealing on the paper or poster we are preparing. The markings of the unit lengths as per the scale must start from zero.
Artistic and Aesthetic Considerations Class 6 Notes
In addition to the steps described in previous sections, there are also some other more artistic and aesthetic aspects one can consider when preparing visual presentations of data to make them more interesting and effective. First, when making a visual presentation of data, such as a pictograph or bar graph, it is important to make it fit in the intended space; this can be controlled, e.g., by choosing the scale appropriately, as we have seen earlier. It is also desirable to make the data presentation visually appealing and easy to understand so that the intended audience appreciates the information being conveyed. Let us consider an example. Here is a table naming the tallest mountain on each continent, along with the height of each mountain in meters.
How much taller is Mount Everest than Mount Kosciuszko? Are Mount Denali and Mount Kilimanjaro very different in height? This is not so easy to quickly discern from a large table of numbers. As we have seen earlier, we can convert the table of numbers into a bar graph, as shown on the right. Here, each value is drawn as a horizontal box. These are longer or shorter depending on the number they represent. This makes it easier to compare the heights of all these mountains at a glance.
However, since the boxes represent heights, it is better and more visually appealing to rotate the picture, so that the boxes grow upward vertically from the ground like mountains. A bar graph with vertical bars is also called a column graph. Columns are the pillars you find in a building that holds up the roof. Below is a column graph for our table of tallest mountains. From this column graph, it becomes easier to compare and visualize the heights of the mountains.
In general, it is more intuitive, suggestive, and visually appealing to represent heights, that are measured upwards from the ground, using bar graphs that have vertical bars or columns. Similarly, lengths that are parallel to the ground (e.g., distances between locations on Earth) are usually best represented using bar graphs with horizontal ars.
Infographics
When data visualizations such as bar graphs are further beautified with more extensive artistic and visual imagery, they are called information graphics, or infographics for short. Infographics aim to make use of attention-attracting and engaging visuals to communicate information even more clearly and quickly, in a visually pleasing way. As an example of how infographics can be used to communicate data even more suggestively, let us go back to the table above listing the tallest mountain on each continent. We drew a bar graph with vertical bars (columns), rather than horizontal bars, to be more indicative of mountains. But instead of rectangles, we could instead use triangles, which look a bit more like mountains. And we can add a splash of colour as well. Here is the result.
While this infographic might look more appealing and suggestive at first glance, it does have some issues. The goal of our bar graph earlier was to represent the heights of various mountains – using bars of the appropriate heights but the same widths. The purpose of using the same widths was to make it clear that we are only comparing heights. However, in this infographic, the taller triangles are also wider! Are taller mountains always wider? The infographic implies additional information that may be misleading and may or may not be correct. Sometimes going for more appealing pictures can also accidentally mislead.
Taking this idea further, and to make the picture even more visually stimulating and suggestive, we can further change the shapes of the mountains to make them look even more like mountains, and add other details, while attempting to preserve the heights. For example, we can create an imaginary mountain range that contains all these mountains. Is the infographic below better than the column graph with rectangular columns of equal width? The mountains look more realistic, but is the picture accurate? For example, Everest appears to be twice as tall as Elbrus.
What is 5642 × 2?
While preparing visually appealing presentations of data, we also need to be careful that the pictures we draw do not mislead us about the facts. In general, it is important to be careful when making or reading infographics, so that we do not mislead our intended audiences and so that we, ourselves, are not misled.
