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Smart Charts - Bar Graphs

Grade 5CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A Bar Graph is a visual tool used to represent data using rectangular bars. These bars can be drawn vertically or horizontally, where the height or length of each bar represents a specific numerical value.

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The graph consists of two main lines called axes. The horizontal line at the bottom is the X-axis (usually for categories like names of fruits or days), and the vertical line on the left is the Y-axis (usually for numbers or frequencies).

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A Scale is the most important part of a bar graph. Since we cannot always draw 100100 centimeters for 100100 items, we use a scale like 1 unit length=10 students1 \text{ unit length} = 10 \text{ students}. This determines how many units each mark on the Y-axis represents.

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All bars in a bar graph must have an equal width. Additionally, the spacing or gaps between the bars should be uniform. This visual consistency helps in comparing the data accurately at a single glance.

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Every bar graph must have a clear Title at the top to explain what the data is about, and Labels on both the X-axis and Y-axis to identify the categories and the units of measurement.

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Data for bar graphs is often organized using Tally Marks. In this system, four vertical lines with one diagonal line across them (∣∣∣∣|||| with a slash) represents a group of 55. These tallies are counted to determine the height of the bars.

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Interpreting a bar graph involves looking at the top of a bar and following a straight horizontal line to the Y-axis to read the number. Visually, the tallest bar represents the 'Most Popular' or 'Maximum' category, while the shortest bar represents the 'Least Popular' or 'Minimum'.

📐Formulae

Value of a category=Number of units on Y-axis×Scale factor\text{Value of a category} = \text{Number of units on Y-axis} \times \text{Scale factor}

Total Data=Sum of values of all individual bars\text{Total Data} = \text{Sum of values of all individual bars}

Difference between two categories=Value of Bar A−Value of Bar B\text{Difference between two categories} = \text{Value of Bar A} - \text{Value of Bar B}

💡Examples

Problem 1:

A bar graph shows the number of students who like different sports. The scale is 1 cm=5 students1 \text{ cm} = 5 \text{ students}. If the bar for 'Cricket' is 4 cm4 \text{ cm} tall and the bar for 'Football' is 3 cm3 \text{ cm} tall, find the total number of students who like these two sports.

Solution:

Step 1: Calculate the number of students who like Cricket. Cricket students=4 cm×5=20 students\text{Cricket students} = 4 \text{ cm} \times 5 = 20 \text{ students} Step 2: Calculate the number of students who like Football. Football students=3 cm×5=15 students\text{Football students} = 3 \text{ cm} \times 5 = 15 \text{ students} Step 3: Find the total sum. Total=20+15=35 students\text{Total} = 20 + 15 = 35 \text{ students}

Explanation:

We use the scale factor to convert the visual height of the bars (in cm) into the actual number of students before adding them together.

Problem 2:

In a class, the number of students who own pets are: Dog (1212), Cat (88), and Fish (44). If you draw a bar graph with a scale of 1 unit=2 students1 \text{ unit} = 2 \text{ students}, how many units high will the bar for 'Cat' be, and how many more students have Dogs than Fish?

Solution:

Step 1: Find the height of the 'Cat' bar. Height=Number of CatsScale=82=4 units\text{Height} = \frac{\text{Number of Cats}}{\text{Scale}} = \frac{8}{2} = 4 \text{ units} Step 2: Calculate the difference between Dog owners and Fish owners. Difference=12−4=8 students\text{Difference} = 12 - 4 = 8 \text{ students}

Explanation:

To find the height of a bar for a graph, divide the actual value by the scale. To find 'how many more', subtract the smaller value from the larger value.