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Data Handling - Bar Graphs

Grade 4ICSE

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

🔑Concepts

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

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The graph is built on two perpendicular lines called axes. The horizontal line is the xx-axis (usually representing categories like names or months), and the vertical line is the yy-axis (usually representing the numerical count or frequency).

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The Scale is the most critical visual component of a bar graph. It defines what 11 unit of length on the graph represents in real numbers. For example, if the data includes large numbers like 100100 and 200200, a scale might be set as 1 unit=20 items1 \text{ unit} = 20 \text{ items}.

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Visually, all bars in a single graph must have a uniform width. The gaps between the bars must also be equal to ensure the graph is neat and easy to read without causing confusion between different categories.

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Every bar graph requires a clear Title at the top to explain what data is being presented, and Axis Labels to identify what is being measured on the xx-axis and yy-axis.

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To interpret a bar graph, you look at the top of a bar and move horizontally to the left to see which number it aligns with on the yy-axis. This value, relative to the scale, tells you the exact quantity for that category.

📐Formulae

Actual Value=Height of the Bar (in units)×Scale Factor\text{Actual Value} = \text{Height of the Bar (in units)} \times \text{Scale Factor}

Number of units for a bar=Actual Data ValueScale Value\text{Number of units for a bar} = \frac{\text{Actual Data Value}}{\text{Scale Value}}

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

Difference=Value of Higher Bar−Value of Lower Bar\text{Difference} = \text{Value of Higher Bar} - \text{Value of Lower Bar}

💡Examples

Problem 1:

The following data shows the number of ice cream cones sold in a week: Vanilla (2525), Chocolate (4040), and Strawberry (3030). If a bar graph is drawn with a scale of 1 unit=5 cones1 \text{ unit} = 5 \text{ cones}, how many units high will the bar for 'Chocolate' be, and what is the total number of cones sold?

Solution:

Step 1: Identify the value for Chocolate, which is 4040 cones. Step 2: Use the scale formula: Units for Chocolate=405=8\text{Units for Chocolate} = \frac{40}{5} = 8 units. Step 3: Calculate the total number of cones: 25+40+30=9525 + 40 + 30 = 95 cones. Step 4: The Chocolate bar will be 88 units high and the total sales are 9595 cones.

Explanation:

We divide the specific category value by the scale factor to find the physical height of the bar on the graph paper and add all values for the total.

Problem 2:

In a school library, there are 5050 Mystery books, 3030 Science books, and 2020 History books. In a bar graph representing this, how much taller (in units) is the Mystery bar than the History bar if the scale is 1 unit=10 books1 \text{ unit} = 10 \text{ books}?

Solution:

Step 1: Find the height of the Mystery bar: 5010=5\frac{50}{10} = 5 units. Step 2: Find the height of the History bar: 2010=2\frac{20}{10} = 2 units. Step 3: Find the difference in units: 5−2=35 - 2 = 3 units. Step 4: Alternatively, find the difference in books first: 50−20=3050 - 20 = 30 books, then convert to units: 3010=3\frac{30}{10} = 3 units.

Explanation:

The difference in the visual height of bars corresponds directly to the difference in the actual data values divided by the chosen scale.