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Data Handling - Drawing a Bar Graph

Grade 6CBSE

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

🔑Concepts

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A bar graph is a pictorial representation of numerical data using bars of uniform width drawn horizontally or vertically with equal spacing between them. The length of each bar represents the frequency or value of the observation.

A basic bar graph structure showing vertical bars of different heights on a coordinate plane.
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Choosing a scale is crucial for drawing an accurate bar graph. A scale is the ratio between the unit length of the bar and the actual value it represents. For example, 1 unit length=10 units1 \text{ unit length} = 10 \text{ units} means a bar of 44 units length represents a value of 4040.

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The width of the bars must be uniform across the graph, and the gap between any two consecutive bars must remain constant to ensure clear comparison.

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Every bar graph must have a Title explaining what the data represents, and both the horizontal (X-axis) and vertical (Y-axis) should be clearly labeled with the scale mentioned.

📐Formulae

Number of units for a bar=Value of the observationValue of 1 unit of scale\text{Number of units for a bar} = \frac{\text{Value of the observation}}{\text{Value of 1 unit of scale}}

Value of observation=Number of units×Value of 1 unit of scale\text{Value of observation} = \text{Number of units} \times \text{Value of 1 unit of scale}

Scale=Maximum Data ValueAvailable space on axis (in units)\text{Scale} = \frac{\text{Maximum Data Value}}{\text{Available space on axis (in units)}}

💡Examples

Problem 1:

The following data shows the number of bicycles sold by a shop in four days: Monday: 35, Tuesday: 20, Wednesday: 25, Thursday: 30. Draw a bar graph for this data using a scale of 1 unit length=5 bicycles1\text{ unit length} = 5\text{ bicycles}.

Solution:

Step 1: Choose the scale, which is 1 unit=5 bicycles1\text{ unit} = 5\text{ bicycles}. Step 2: Calculate the height of the bars for each day:

  • Monday: 355=7 units\frac{35}{5} = 7\text{ units}
  • Tuesday: 205=4 units\frac{20}{5} = 4\text{ units}
  • Wednesday: 255=5 units\frac{25}{5} = 5\text{ units}
  • Thursday: 305=6 units\frac{30}{5} = 6\text{ units} Step 3: Draw two perpendicular axes. Mark 'Days' on the X-axis and 'Number of Bicycles' on the Y-axis. Step 4: Draw bars of equal width with heights 7,4,5, and 67, 4, 5, \text{ and } 6 units respectively, keeping equal gaps between them.

Explanation:

To represent the data accurately, we divide each data value by the scale factor to find the physical height of the bars. This ensures the proportions are maintained correctly on the graph paper.

Problem 2:

A student spends time on various activities in a day: Study (6 hours), Play (2 hours), Sleep (8 hours), Others (8 hours). If we represent this on a bar graph with a scale of 1 unit=2 hours1\text{ unit} = 2\text{ hours}, what will be the heights of the bars?

Solution:

Given scale: 1 unit=2 hours1\text{ unit} = 2\text{ hours}. Heights of bars:

  • Study: 62=3 units\frac{6}{2} = 3\text{ units}
  • Play: 22=1 unit\frac{2}{2} = 1\text{ unit}
  • Sleep: 82=4 units\frac{8}{2} = 4\text{ units}
  • Others: 82=4 units\frac{8}{2} = 4\text{ units}

Explanation:

Each activity's duration is divided by the value of one unit (22 hours) to determine how many units high each bar should be drawn on the Y-axis.

Problem 3:

The number of students in different clubs of a school are: Sports (40), Music (25), Arts (30), and Dance (15). Draw a bar graph representing this data using a scale of 1 unit length=5 students1 \text{ unit length} = 5 \text{ students}.

Bar graph showing students in clubs: Sports(40), Music(25), Arts(30), and Dance(15).

Solution:

  1. Identify the categories for the horizontal axis: Sports, Music, Arts, Dance.
  2. Determine the bar heights based on the scale 1 unit=5 students1 \text{ unit} = 5 \text{ students}:
  • Sports: 40÷5=8 units40 \div 5 = 8 \text{ units}
  • Music: 25÷5=5 units25 \div 5 = 5 \text{ units}
  • Arts: 30÷5=6 units30 \div 5 = 6 \text{ units}
  • Dance: 15÷5=3 units15 \div 5 = 3 \text{ units}
  1. Draw the bars with equal width and equal spacing on the graph.

Explanation:

By using a scale of 55, we convert large numbers into manageable unit lengths. For example, the Sports bar is the tallest at 88 units because 8×5=408 \times 5 = 40.

Problem 4:

A fruit seller sold the following quantities of fruits in a day: Mango (50 kg), Apple (30 kg), Orange (40 kg), and Grapes (20 kg). Draw a bar graph for this data using a scale of 1 unit length=10 kg1 \text{ unit length} = 10 \text{ kg}.

Bar graph of fruit sales where M=50, A=30, O=40, G=20.

Solution:

  1. Categories: Mango, Apple, Orange, Grapes.
  2. Bar heights calculation (1 unit=10 kg1 \text{ unit} = 10 \text{ kg}):
  • Mango: 50÷10=5 units50 \div 10 = 5 \text{ units}
  • Apple: 30÷10=3 units30 \div 10 = 3 \text{ units}
  • Orange: 40÷10=4 units40 \div 10 = 4 \text{ units}
  • Grapes: 20÷10=2 units20 \div 10 = 2 \text{ units}

Explanation:

Each unit on the vertical axis represents 10 kg10 \text{ kg}. The Mango bar reaches the 5th5^{th} unit line, representing 50 kg50 \text{ kg}, which is the highest quantity sold.