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Data Handling and Presentation - 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. The lengths or heights of these bars are proportional to the values they represent.

A basic bar graph showing three categories A, B, and C with heights of 8, 4, and 6 respectively.
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The scale is the most important part of a bar graph. It defines how many units of data are represented by one unit of length on the axis. For example, 1 unit length=10 units1 \text{ unit length} = 10 \text{ units}.

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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.

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The axes must be clearly labeled. Usually, the horizontal axis (x-axis) represents the categories, and the vertical axis (y-axis) represents the numerical values or frequencies.

📐Formulae

Height of a bar=Value of the dataValue represented by 1 unit length\text{Height of a bar} = \frac{\text{Value of the data}}{\text{Value represented by 1 unit length}}

Value of data=Height of the bar×Scale unit\text{Value of data} = \text{Height of the bar} \times \text{Scale unit}

Scale:1 unit length=n units of the given quantity\text{Scale}: 1 \text{ unit length} = n \text{ units of the given quantity}

💡Examples

Problem 1:

The following table shows the number of bicycles sold by a shop in four different months: July (4545), August (6060), September (3535), and October (5050). Choose a suitable scale and determine the heights of the bars for a vertical bar graph.

Solution:

  1. Let us choose a scale: 1 unit length=10 bicycles1 \text{ unit length} = 10 \text{ bicycles}.
  2. Calculate the height for each month:
  • July: 4510=4.5 units\frac{45}{10} = 4.5 \text{ units}
  • August: 6010=6 units\frac{60}{10} = 6 \text{ units}
  • September: 3510=3.5 units\frac{35}{10} = 3.5 \text{ units}
  • October: 5010=5 units\frac{50}{10} = 5 \text{ units}

Explanation:

To determine the height of the bars, we divide the actual data value by the chosen scale. Since the highest value is 6060, a scale of 1010 makes the graph compact and easy to read.

Problem 2:

In a bar graph where the scale is 1 unit length=5 students1 \text{ unit length} = 5 \text{ students}, if the bar representing 'Grade 6' has a height of 99 units, how many students are there in Grade 6?

Solution:

Given:

  • Scale: 1 unit length=5 students1 \text{ unit length} = 5 \text{ students}
  • Height of the bar =9 units= 9 \text{ units}

Number of students=9×5=45 students\text{Number of students} = 9 \times 5 = 45 \text{ students}

Explanation:

By multiplying the number of units shown on the graph by the value of a single unit defined in the scale, we obtain the actual quantity.

Problem 3:

The following data shows the favorite sports of 300300 students: Cricket (120120), Football (8080), and Tennis (100100). Represent this data on a bar graph by choosing a scale of 1 unit length=20 students1 \text{ unit length} = 20 \text{ students}.

Bar graph of sports preferences where Cricket is 120, Football is 80, and Tennis is 100.

Solution:

  1. Identify the values: Cricket = 120120, Football = 8080, Tennis = 100100.
  2. Calculate bar heights using the scale 1 unit=201 \text{ unit} = 20:
    • Cricket: 120÷20=6120 \div 20 = 6 units
    • Football: 80÷20=480 \div 20 = 4 units
    • Tennis: 100÷20=5100 \div 20 = 5 units
  3. Draw the bars with heights 66, 44, and 55 respectively.

Explanation:

By dividing each value by the scale factor of 2020, we find the height in units required for each bar on the graph paper.

Problem 4:

Observe the bar graph which shows the marks obtained by a student in different subjects. Find the marks in Mathematics if the scale is 1 unit length=10 marks1 \text{ unit length} = 10 \text{ marks} and the bar height for Mathematics is 8.58.5 units.

A bar graph showing the bar for Mathematics reaching the 85 mark on the vertical axis.

Solution:

Marks=Height of bar×Scale factor\text{Marks} = \text{Height of bar} \times \text{Scale factor} Marks in Mathematics=8.5×10=85\text{Marks in Mathematics} = 8.5 \times 10 = 85 The student obtained 8585 marks in Mathematics.

Explanation:

To find the actual data value from a graph, multiply the measured height of the bar by the value assigned to one unit length in the scale.