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Data Handling - Bar Graphs

Grade 5ICSE

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

🔑Concepts

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A Bar Graph is a pictorial representation of data using rectangular bars of uniform width. These bars can be drawn vertically or horizontally, where the length or height of the bar represents the numerical value of the data.

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The Horizontal Axis (X-axis) and Vertical Axis (Y-axis) form the framework of the graph. Usually, the categories or items being measured are placed on the X-axis, while the numerical values (frequency) are marked on the Y-axis.

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The Scale is a predefined ratio used to represent large numbers in a small space. For example, if we cannot draw a bar 50extcm50 ext{ cm} long, we use a scale like 1extunitlength=10extunitsofdata1 ext{ unit length} = 10 ext{ units of data}, meaning a 5extunit5 ext{ unit} tall bar represents 5050 units.

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Uniformity is essential in bar graphs: all bars must have the same width, and the gaps between any two adjacent bars must be equal throughout the graph.

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Labels and Titles are mandatory components. A title explains what the graph is about (e.g., 'Favorite Fruits of Students'), and axis labels identify what the categories (e.g., 'Fruits') and numbers (e.g., 'Number of Students') represent.

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Data Interpretation involves analyzing the heights of the bars to draw conclusions. The tallest bar represents the maximum value (mode), while the shortest bar represents the minimum value in the data set.

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To draw a bar graph, first identify the maximum value in the data to choose an appropriate scale, then draw the axes, mark the points at equal intervals, and finally draw the rectangular bars up to the calculated heights.

📐Formulae

Number of units for a bar=Value of the dataScale value\text{Number of units for a bar} = \frac{\text{Value of the data}}{\text{Scale value}}

Actual Value=Number of units (height/length)×Scale value\text{Actual Value} = \text{Number of units (height/length)} \times \text{Scale value}

Total Frequency=∑Values of all bars\text{Total Frequency} = \sum \text{Values of all bars}

💡Examples

Problem 1:

In a class of 4040 students, the number of students who like different flavors of ice cream is as follows: Vanilla: 1515, Chocolate: 1010, Mango: 1010, and Strawberry: 55. If you are drawing a bar graph with a scale of 1 unit=5 students1 \text{ unit} = 5 \text{ students}, calculate the height of each bar.

Solution:

  1. Height of Vanilla bar = 155=3 units\frac{15}{5} = 3 \text{ units} \ 2. Height of Chocolate bar = 105=2 units\frac{10}{5} = 2 \text{ units} \ 3. Height of Mango bar = 105=2 units\frac{10}{5} = 2 \text{ units} \ 4. Height of Strawberry bar = 55=1 unit\frac{5}{5} = 1 \text{ unit}

Explanation:

To find the height of each bar, we divide the actual data value by the scale value chosen for the Y-axis.

Problem 2:

A bar graph shows the number of books sold by a shopkeeper in four days. The scale is 1 cm=12 books1 \text{ cm} = 12 \text{ books}. If the bar for 'Wednesday' is 6 cm6 \text{ cm} long, how many books were sold on that day?

Solution:

  1. Given Scale: 1 cm=12 books1 \text{ cm} = 12 \text{ books} \ 2. Height of the bar for Wednesday = 6 cm6 \text{ cm} \ 3. Total books sold = 6×12=72 books6 \times 12 = 72 \text{ books}

Explanation:

To find the actual quantity from a graph, multiply the measured length of the bar by the value of the scale.