Data Handling Ex 9.4: A Step-by-Step Guide for Class 6

Understanding Bar Graphs

A bar graph (or bar chart) is a picture that represents data using rectangular bars. The height or length of these bars is proportional to the values they represent. It's like telling a story with blocks! Bar graphs are excellent for comparing different categories of information at a glance.

A bar graph has two main lines, called axes:

1. The Horizontal Axis (X-axis): This is the line that goes from left to right. We usually show the categories we are comparing here (like names of fruits, subjects, or days of the week).
2. The Vertical Axis (Y-axis): This is the line that goes from bottom to top. It represents the numbers or values (like the number of students, marks obtained, or temperature).

The most important part is the scale. The scale on the Y-axis tells us what each unit of height means. For example, a scale of '1 unit = 5 books' means that a bar that is 3 units tall represents 3 x 5 = 15 books. By looking at the heights of the different bars, you can instantly see which category has the highest value and which has the lowest.

How to Draw a Bar Graph: Step-by-Step

1. Step 1: Collect Data and Draw Axes — First, gather your data in a table. Then, use a ruler to draw two perpendicular lines on a graph paper – a horizontal line (X-axis) and a vertical line (Y-axis). Let them meet at a point 'O'.
2. Step 2: Choose a Suitable Scale — Look at the highest value in your data. Choose a scale for the Y-axis that lets you fit all the data on the page. For example, if your highest value is 85, you could choose a scale of 1 unit = 10 marks. Always write the scale clearly on the graph.
3. Step 3: Label the Axes — Label the X-axis with the categories you are comparing (e.g., 'Subjects'). Label the Y-axis with what the numbers represent (e.g., 'Marks Obtained').
4. Step 4: Draw the Bars — On the X-axis, mark points for each category at equal distances. For each category, draw a rectangular bar. The height of the bar should match its value on the Y-axis scale. Make sure all bars have the same width and the space between them is equal.
5. Step 5: Give it a Title — Finally, give your bar graph a clear title at the top that explains what the graph is about (e.g., 'Marks Obtained in Final Exams').

Worked Example: Interpreting a Bar Graph

• Imagine a bar graph shows the number of cars sold by a company in the first five months of the year. The X-axis shows the months (Jan, Feb, Mar, Apr, May) and the Y-axis shows the 'Number of Cars Sold' with a scale of 1 unit = 50 cars. Data from the graph: - Jan: Bar height is 3 units. - Feb: Bar height is 5 units. - Mar: Bar height is 4 units. - Apr: Bar height is 6 units. - May: Bar height is 2 units. Question 1: How many cars were sold in April? Solution: The bar for April has a height of 6 units. The scale is 1 unit = 50 cars. So, cars sold in April = 6 x 50 = 300 cars. Question 2: In which month were the minimum number of cars sold? Solution: Look for the shortest bar. The bar for May is the shortest, with a height of 2 units. So, the minimum number of cars were sold in May. Question 3: What is the difference between the number of cars sold in February and March? Solution: - Cars sold in Feb = 5 units x 50 = 250 cars. - Cars sold in Mar = 4 units x 50 = 200 cars. - Difference = 250 - 200 = 50 cars.

Key Points for Perfect Bar Graphs

• Always use a pencil and a ruler to draw neat and straight lines.
• The width of all the bars must be the same. Don't draw some bars thin and others thick.
• The distance or gap between any two consecutive bars must be the same.
• Choosing the right scale is crucial. A poorly chosen scale can make the graph hard to read or misleading.
• Always label both axes and give a suitable title to the graph.
• If the numbers are very large (like 2500, 3000), you must use a scale like '1 unit = 500' to make the graph fit on the paper.

Practice Questions with Solutions

• Q: The number of students in different clubs in a school is given below: - Music Club: 60 - Dance Club: 45 - Art Club: 75 - Sports Club: 90 Draw a bar graph to represent this data. (Choose scale: 1 unit = 15 students) A: Step 1: Draw the X-axis and Y-axis. Label the X-axis as 'Clubs' and the Y-axis as 'Number of Students'. Step 2: Write the chosen scale '1 unit = 15 students' at the top corner of the graph. Step 3: On the Y-axis, mark points at equal intervals like 15, 30, 45, 60, 75, 90. Step 4: On the X-axis, mark the names of the clubs at equal gaps. Step 5: Draw the bars. - Music Club: Height will correspond to 60 on the Y-axis. - Dance Club: Height will correspond to 45. - Art Club: Height will correspond to 75. - Sports Club: Height will correspond to 90. Step 6: Give the title 'Students in Different School Clubs'. Final answer: A bar graph with four bars of uniform width and spacing, representing the data accurately with all labels and a title.
• Q: The following bar graph shows the runs scored by a cricket team in the first 5 overs. Read the graph and answer the questions. (Assume a graph where Over 1=6 runs, Over 2=14 runs, Over 3=4 runs, Over 4=18 runs, Over 5=10 runs) (i) What information is given by the bar graph? (ii) In which over were the maximum runs scored? (iii) What is the total score after 5 overs? A: Step 1: (i) To find the information given, read the title and the labels on the axes. The graph shows the runs scored by a cricket team in each of the first 5 overs of a match. Step 2: (ii) To find the maximum runs, locate the tallest bar. The tallest bar is for 'Over 4', which corresponds to 18 runs. Step 3: (iii) To find the total score, add the runs from all 5 overs by reading the height of each bar: 6 (Over 1) + 14 (Over 2) + 4 (Over 3) + 18 (Over 4) + 10 (Over 5) = 52 runs. Final answer: (i) The graph shows runs scored in each of the first 5 overs. (ii) Maximum runs were scored in Over 4. (iii) The total score after 5 overs is 52.
• Q: The marks obtained by Sunita in her half-yearly examination out of 100 are: - English: 75 - Hindi: 80 - Maths: 95 - Science: 85 - Social Studies: 70 Draw a bar graph to represent the above data. A: Step 1: Draw the X-axis (Subjects) and Y-axis (Marks). Since the highest mark is 95, a suitable scale would be 1 unit = 10 marks. Step 2: Label the axes and write the scale '1 unit = 10 marks' on the graph. Mark 10, 20, 30,... up to 100 on the Y-axis. Step 3: Draw a bar for English up to the height of 75. This will be halfway between 70 and 80. Step 4: Draw bars for Hindi (height 80), Maths (height 95 - halfway between 90 and 100), Science (height 85 - halfway between 80 and 90), and Social Studies (height 70). Step 5: Ensure all bars have the same width and are equally spaced. Add the title 'Sunita's Half-Yearly Exam Marks'. Final answer: A complete bar graph showing Sunita's marks in five subjects with the correct scale, labels, and title.
• Q: A survey of 120 school students was done to find which activity they prefer to do in their free time. - Playing: 45 - Reading story books: 30 - Watching TV: 20 - Listening to music: 10 - Painting: 15 Draw a bar graph to illustrate the data taking a scale of 1 unit = 5 students. A: Step 1: Draw and label the axes. X-axis for 'Preferred Activity' and Y-axis for 'Number of Students'. Step 2: Write the scale: '1 unit = 5 students'. Mark the Y-axis from 0 up to 50 at intervals of 5 (5, 10, 15, ...). Step 3: On the X-axis, represent each activity. Step 4: Draw the bars corresponding to the data: - Playing: Height up to 45. - Reading: Height up to 30. - Watching TV: Height up to 20. - Listening to music: Height up to 10. - Painting: Height up to 15. Step 5: Give the graph a title: 'Preferred Free Time Activities of Students'. Final answer: A bar graph correctly representing the preferences of 120 students with all necessary components like title, scale, and labeled axes.

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