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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 visual representation of data using rectangular bars of uniform width, where the lengths (heights) are proportional to the values they represent.

A basic bar graph showing vertical bars of different heights on a set of axes.
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Choosing an appropriate scale is crucial. If the data values range from 00 to 500500, a scale of 1 unit=501 \text{ unit} = 50 is better than 1 unit=11 \text{ unit} = 1. The scale determines how many actual units one division on the yy-axis represents.

A vertical axis showing a scale where 1 unit represents 100 units of data.
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In a Bar Graph, the width of the bars and the spacing between them must be uniform to ensure clarity and accurate comparison of the data points.

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Double Bar Graphs are used to compare two sets of data simultaneously. For example, comparing the sales of two different products over several months using pairs of adjacent bars.

Double bar graph showing pairs of bars side-by-side for comparison.

📐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.

Problem 3:

The following data shows the number of cars sold by a showroom over three months: January: 150150, February: 250250, March: 200200. Construct a bar graph. What is the height of the bar for February if the scale is 1 unit=50 cars1 \text{ unit} = 50 \text{ cars}?

Bar graph showing car sales for Jan (3 units), Feb (5 units), and Mar (4 units).

Solution:

  1. Identify the values: Jan = 150150, Feb = 250250, Mar = 200200.
  2. Given scale: 1 unit=50 cars1 \text{ unit} = 50 \text{ cars}.
  3. Calculate height for February: 25050=5 units\frac{250}{50} = 5 \text{ units}.
  4. Heights for others: Jan = 15050=3 units\frac{150}{50} = 3 \text{ units}, Mar = 20050=4 units\frac{200}{50} = 4 \text{ units}.

Explanation:

The height of each bar is determined by dividing the actual value by the scale factor. For February, 250÷50=5250 \div 50 = 5 units on the graph.

Problem 4:

A survey of 400400 students shows their favorite fruits: Mango: 160160, Apple: 120120, Orange: 8080, Banana: 4040. If a bar graph is drawn with a scale of 1 unit=20 students1 \text{ unit} = 20 \text{ students}, find the difference in heights between the bars for Mango and Banana.

Bar graph of favorite fruits with Mango at 8 units and Banana at 2 units.

Solution:

  1. Scale: 1 unit=20 students1 \text{ unit} = 20 \text{ students}.
  2. Height of Mango bar = 16020=8 units\frac{160}{20} = 8 \text{ units}.
  3. Height of Banana bar = 4020=2 units\frac{40}{20} = 2 \text{ units}.
  4. Difference in heights = 8−2=6 units8 - 2 = 6 \text{ units}.

Explanation:

We first convert the number of students into graph units using the scale. Mango requires 8 units and Banana requires 2 units. The difference is 8−2=68 - 2 = 6 units.