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

A basic bar graph showing vertical bars of different heights on a grid.
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Every bar graph must have a 'Scale'. The scale tells us how many units of data are represented by a unit length of the bar (e.g., 1 unit=10 items1\text{ unit} = 10\text{ items}). All bars must have uniform width and equal spacing between them.

Illustration showing a scale definition for a bar graph.
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Bar graphs can be drawn vertically or horizontally. In a vertical bar graph, the bars stand on the xx-axis and their height represents the value. In a horizontal bar graph, the bars start from the yy-axis and their length represents the value.

A horizontal bar graph representation.
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Data collection is the first step. Data is usually organized in a frequency table before being plotted on the graph. The bars are then drawn according to the frequencies recorded in the table.

📐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.

Problem 3:

The following data shows the marks obtained by a student in three subjects: Math (9090), Science (7070), and English (8080). Draw a vertical bar graph using the scale 1 unit=10 marks1\text{ unit} = 10\text{ marks}.

Bar graph showing marks: Math 90, Science 70, English 80.

Solution:

  1. Identify the values: Math =90= 90, Science =70= 70, English =80= 80.
  2. Determine the height of bars based on the scale (1 unit=10 marks1\text{ unit} = 10\text{ marks}): Math: 90÷10=9 units90 \div 10 = 9\text{ units} Science: 70÷10=7 units70 \div 10 = 7\text{ units} English: 80÷10=8 units80 \div 10 = 8\text{ units}
  3. Draw the bars on the graph with heights 99, 77, and 88 respectively.

Explanation:

Since each unit on the yy-axis represents 1010 marks, we divide the total marks by 1010 to find the number of units to plot for each subject.

Problem 4:

A fruit seller sold 4040 kg of Apples, 3030 kg of Mangoes, and 5050 kg of Bananas. If the bar for Bananas is 10 cm10\text{ cm} long in a horizontal bar graph, find the scale used and the length of the bar for Mangoes.

Horizontal bar graph showing fruit sales with proportional bar lengths.

Solution:

  1. For Bananas: Value =50 kg= 50\text{ kg}, Bar length =10 cm= 10\text{ cm}.
  2. Scale =Value÷Length=50÷10=5 kg per cm= \text{Value} \div \text{Length} = 50 \div 10 = 5\text{ kg per cm}.
  3. Length for Mangoes: Value =30 kg= 30\text{ kg}.
  4. Length =Value÷Scale=30÷5=6 cm= \text{Value} \div \text{Scale} = 30 \div 5 = 6\text{ cm}.

Explanation:

By comparing the actual quantity of Bananas to the bar length, we find the scale (1 cm=5 kg1\text{ cm} = 5\text{ kg}). We then use this scale to determine that the 30 kg30\text{ kg} of Mangoes requires a 6 cm6\text{ cm} bar.