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Data Handling - Use of Bar Graphs with appropriate scale

Grade 7CBSE

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. Imagine a series of rectangles standing on a base line (the X-axis), where the height of each rectangle corresponds to the numerical value it represents.

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The Horizontal Axis (X-axis) and Vertical Axis (Y-axis) form the framework. Typically, categories or items being compared are placed on the horizontal axis, while the frequency or numerical values are placed on the vertical axis. The point where they meet is the origin (0,0)(0,0).

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Choosing an Appropriate Scale is essential for fitting data on graph paper. The scale is the ratio of the length of the bar to the actual value. For example, if your highest data value is 100100 and you have 1010 grid lines, a scale of 1 unit=10 units1 \text{ unit} = 10 \text{ units} would be appropriate.

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Uniformity of Bars and Spacing is a strict rule. Every bar must have the exact same width, and the distance between any two adjacent bars must be kept equal. This visual consistency ensures that the viewer focuses only on the heights, which represent the data values.

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Double Bar Graphs are used specifically for comparing two sets of data on the same categories simultaneously. For example, comparing the number of boys and girls in different classes. Visually, this appears as two bars of different colors or shades standing side-by-side for each category on the X-axis.

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Interpretation involves reading the top edge of a bar and tracing it horizontally to the Y-axis to find the corresponding number. By looking at the relative heights of different bars, one can instantly identify the 'maximum' (tallest bar) and 'minimum' (shortest bar) values in a data set.

📐Formulae

Length of a bar (in units)=Actual Data ValueValue per Unit (Scale)\text{Length of a bar (in units)} = \frac{\text{Actual Data Value}}{\text{Value per Unit (Scale)}}

Actual Data Value=Length of the bar (in units)×Scale Factor\text{Actual Data Value} = \text{Length of the bar (in units)} \times \text{Scale Factor}

Scale Factor=Maximum ValueTotal number of units on the axis\text{Scale Factor} = \frac{\text{Maximum Value}}{\text{Total number of units on the axis}}

💡Examples

Problem 1:

The number of students in five different classes are: Class 6: 4040, Class 7: 4545, Class 8: 3535, Class 9: 3030, Class 10: 2525. If you are drawing a bar graph with a scale of 1 unit=5 students1 \text{ unit} = 5 \text{ students}, what will be the heights of the bars for Class 7 and Class 10?

Solution:

  1. Identify the scale: 1 unit=5 students1 \text{ unit} = 5 \text{ students}.
  2. For Class 7: Height = Number of studentsScale=455=9 units\frac{\text{Number of students}}{\text{Scale}} = \frac{45}{5} = 9 \text{ units}.
  3. For Class 10: Height = Number of studentsScale=255=5 units\frac{\text{Number of students}}{\text{Scale}} = \frac{25}{5} = 5 \text{ units}.

Explanation:

To determine the height of the bars on the graph, divide the actual data value by the value represented by one unit of the scale.

Problem 2:

A double bar graph compares the marks of a student in Term 1 and Term 2. For Mathematics, the Term 1 bar is 7 units7 \text{ units} high and the Term 2 bar is 8.5 units8.5 \text{ units} high. If the scale is 1 unit=10 marks1 \text{ unit} = 10 \text{ marks}, calculate the increase in marks.

Solution:

  1. Marks in Term 1 = 7×10=70 marks7 \times 10 = 70 \text{ marks}.
  2. Marks in Term 2 = 8.5×10=85 marks8.5 \times 10 = 85 \text{ marks}.
  3. Increase in marks = 85−70=15 marks85 - 70 = 15 \text{ marks}.

Explanation:

First, convert the bar heights into actual values by multiplying by the scale factor. Then, find the difference between the two values to determine the improvement or change.