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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 visual representation of data using rectangular bars of uniform width, where the height or length of each bar is proportional to the value it represents.

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The graph is drawn on a coordinate plane with two perpendicular lines: the horizontal line is called the X-axis (representing categories) and the vertical line is called the Y-axis (representing numerical values).

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Choosing an appropriate scale is crucial; the scale is the fixed length used to represent a certain number of data units, such as 1 unit length=5 units of data1\text{ unit length} = 5\text{ units of data}.

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All bars in a bar graph must have the same width, and the spacing between any two consecutive bars must be equal to maintain visual consistency.

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The height of a vertical bar (or length of a horizontal bar) is determined by the numerical value of the data point it represents, relative to the chosen scale.

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A complete bar graph must include a clear Title at the top and Labels for both the X-axis and Y-axis to explain what the data and the bars signify.

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When reading a bar graph, look at the top edge of the bar and trace it horizontally to the Y-axis to determine the exact numerical value of that category.

📐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.