krit.club logo

Data Handling - Interpretation of a Bar Graph

Grade 6CBSE

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

🔑Concepts

•

A bar graph is a visual representation of data using rectangular bars of equal width. These bars can be drawn vertically or horizontally with equal spacing between them.

•

The graph consists of two perpendicular lines called axes: the horizontal line is typically the x-axis (categories) and the vertical line is the y-axis (values/frequencies).

•

The height or length of each bar represents the numerical value of the specific category it belongs to. A taller bar in a vertical graph indicates a larger quantity or frequency.

•

A Scale is a crucial component that defines the relationship between the unit length of a bar and the actual numerical value. For example, 1 unit length=10 units1 \text{ unit length} = 10 \text{ units} of the data.

•

To interpret a bar graph, you must look at the top edge of a bar and move horizontally (or vertically for horizontal bars) to the axis with the scale to read the corresponding number.

•

Uniformity is a key visual feature: all bars must have the same width, and the gaps between consecutive bars must be identical throughout the entire graph.

•

The title of the bar graph provides the context of the data being displayed, while labels on each axis explain what the categories and the numerical values represent.

•

Comparative analysis is performed by looking at the relative heights of the bars. The tallest bar represents the maximum value (mode in some contexts), while the shortest bar represents the minimum value.

📐Formulae

Value of a bar=Number of units×Scale factor\text{Value of a bar} = \text{Number of units} \times \text{Scale factor}

Number of units=Actual ValueValue per unit length\text{Number of units} = \frac{\text{Actual Value}}{\text{Value per unit length}}

Total Sum=∑(Individual bar values)\text{Total Sum} = \sum (\text{Individual bar values})

Difference between two categories=Value of Bar A−Value of Bar B\text{Difference between two categories} = \text{Value of Bar A} - \text{Value of Bar B}

💡Examples

Problem 1:

A bar graph represents the number of bicycles sold by a shop in four days. The scale is 1 unit length=5 bicycles1 \text{ unit length} = 5 \text{ bicycles}. If the bar for Monday is 4 units4 \text{ units} long, the bar for Tuesday is 6 units6 \text{ units} long, and the bar for Wednesday is 3 units3 \text{ units} long, find the total number of bicycles sold in these three days.

Solution:

Step 1: Find the number of bicycles sold on each day using the formula Value=Units×Scale\text{Value} = \text{Units} \times \text{Scale}.

  • Monday: 4×5=20 bicycles4 \times 5 = 20 \text{ bicycles}
  • Tuesday: 6×5=30 bicycles6 \times 5 = 30 \text{ bicycles}
  • Wednesday: 3×5=15 bicycles3 \times 5 = 15 \text{ bicycles} Step 2: Calculate the total by adding the daily values. Total = 20+30+15=65 bicycles20 + 30 + 15 = 65 \text{ bicycles}.

Explanation:

We first convert the visual units into actual data values by multiplying the height of each bar by the given scale factor, then sum the results to find the grand total.

Problem 2:

Observe a bar graph where the vertical axis represents 'Marks Obtained' and the horizontal axis represents 'Subjects'. If the bar for Mathematics reaches the 9090 mark and the bar for Science reaches the 7575 mark, how many more marks were obtained in Mathematics than in Science?

Solution:

Step 1: Identify the values from the graph.

  • Marks in Mathematics = 9090
  • Marks in Science = 7575 Step 2: Calculate the difference to find how many 'more' marks were obtained. Difference = 90−75=15 marks90 - 75 = 15 \text{ marks}.

Explanation:

Interpretation involves reading the specific values associated with the height of the bars for the given categories and performing subtraction to find the comparative difference.