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Data Handling and Presentation - Bar Graphs

Grade 6CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A bar graph is a pictorial representation of numerical data using rectangular bars (columns) of equal width, where the length (or height) of each bar is proportional to the value it represents.

A basic bar graph structure showing vertical bars on a coordinate system with X and Y axes labeled.
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The 'Scale' of a bar graph is a chosen ratio that relates the length of the bar to the actual numerical value. For example, 11 unit length = 55 units of data.

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The width of the bars should be kept uniform (the same) for all categories, and the spacing between any two consecutive bars should also be equal.

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The title of the bar graph explains what information is being presented, and the axes should be clearly labeled to indicate the categories and the frequency/values.

📐Formulae

Length of a bar=Numerical Value of the DataValue of 1 unit length (Scale)\text{Length of a bar} = \frac{\text{Numerical Value of the Data}}{\text{Value of 1 unit length (Scale)}}

Value of Data=Length of the bar×Scale unit\text{Value of Data} = \text{Length of the bar} \times \text{Scale unit}

Total Frequency=Sum of all observations\text{Total Frequency} = \text{Sum of all observations}

💡Examples

Problem 1:

The number of marks obtained by Rohan in five subjects are: Hindi: 7575, English: 6060, Maths: 9090, Science: 8080, and S.St: 7070. If we choose a scale of 11 unit length = 1010 marks, find the length of the bar for Maths.

Solution:

Marks in Maths = 9090. Scale = 11 unit length = 1010 marks. Length of the bar for Maths = 9010=9\frac{90}{10} = 9 units.

Explanation:

To find the length of the bar, we divide the actual value of the data by the value assigned to one unit of the scale.

Problem 2:

In a bar graph, the bar representing the number of bicycles sold in a shop is 77 units long. If the scale is 11 unit length = 1515 bicycles, calculate the total number of bicycles sold.

Solution:

Length of the bar = 77 units. Scale = 11 unit = 1515 bicycles. Total bicycles sold = 7×15=1057 \times 15 = 105.

Explanation:

The total value is calculated by multiplying the number of units shown on the graph by the value of each unit.

Problem 3:

The following are the number of electric bulbs purchased for a lodging house during the first four months of a year: January (2020), February (2424), March (3030), April (3434). If we want to represent this data on a bar graph, what would be an appropriate scale?

Solution:

The data values are 20,24,30,3420, 24, 30, 34. Since all values are even and range between 2020 and 3434, an appropriate scale could be 11 unit length = 22 bulbs or 11 unit length = 55 bulbs.

Explanation:

A scale is chosen based on the range of the data so that the bars are neither too long nor too short to fit on the graph paper.

Problem 4:

The number of trees planted by a school in four consecutive years is given: 2020 (150150 trees), 2021 (250250 trees), 2022 (200200 trees), and 2023 (300300 trees). If a scale of 11 unit = 5050 trees is used, calculate the height of the bars for each year and draw the representation.

Bar graph showing tree plantation from 2020 to 2023 with bar heights 3, 5, 4, and 6 units respectively.

Solution:

  1. Given scale: 1 unit=50 trees1 \text{ unit} = 50 \text{ trees}.
  2. For 2020: 15050=3 units\frac{150}{50} = 3 \text{ units}.
  3. For 2021: 25050=5 units\frac{250}{50} = 5 \text{ units}.
  4. For 2022: 20050=4 units\frac{200}{50} = 4 \text{ units}.
  5. For 2023: 30050=6 units\frac{300}{50} = 6 \text{ units}.

Explanation:

To find the length of the bar, we divide the actual value by the scale value. Here, dividing each year's total by 5050 gives us the corresponding height in units for the graph.

Problem 5:

Observe the following bar graph which shows the amount of rainfall (in cm) in a city over 3 months: July (1212 cm), August (1616 cm), and September (88 cm). If the scale is 1 unit=4 cm1 \text{ unit} = 4 \text{ cm}, what is the total rainfall recorded over the three months?

Bar graph showing rainfall for July (3 units), August (4 units), and September (2 units).

Solution:

Total Rainfall=Rainfall in July+Rainfall in August+Rainfall in September\text{Total Rainfall} = \text{Rainfall in July} + \text{Rainfall in August} + \text{Rainfall in September} Total Rainfall=12+16+8=36 cm\text{Total Rainfall} = 12 + 16 + 8 = 36 \text{ cm} Using scale units: July: 3 units×4=12 cm3 \text{ units} \times 4 = 12 \text{ cm} August: 4 units×4=16 cm4 \text{ units} \times 4 = 16 \text{ cm} September: 2 units×4=8 cm2 \text{ units} \times 4 = 8 \text{ cm}

Explanation:

The total rainfall is the sum of the individual values represented by the bars. We calculate each value by multiplying the unit height of the bar by the scale factor.