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Data Handling - Pictographs

Grade 6CBSE

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

🔑Concepts

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Definition of a Pictograph: A pictograph represents data using pictures, icons, or symbols of objects. It is a visual representation where the frequency of data is shown by the number of times a symbol is repeated. Visually, it appears as a table where the first column contains categories and the subsequent rows display horizontal lines of identical icons.

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The Importance of a Key: Since drawing large numbers of items is impractical, a 'Key' is used to define what one symbol represents. For example, a single picture of a book might represent 55 actual books. The key is typically written as 1 symbol=5 units1 \text{ symbol} = 5 \text{ units} and is visually placed at the top or bottom of the chart.

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Data Interpretation: Reading a pictograph involves counting the number of symbols in a row and multiplying that count by the value defined in the key. Visually, if a row for 'Monday' has 66 sun icons and the key states 1 icon=2 hours of sunlight1 \text{ icon} = 2 \text{ hours of sunlight}, the total is 6×2=12 hours6 \times 2 = 12 \text{ hours}.

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Handling Partial Symbols: To represent numbers that are not exact multiples of the key, partial symbols are used. Visually, if a full circle represents 1010 students, a semi-circle (half-circle) represents 55 students. This allows the pictograph to show more precise data values.

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Standardized Icon Sizing: In a well-constructed pictograph, every icon must be the same size and spaced evenly. This ensures that the length of the row visually reflects the quantity, allowing for a quick comparison between categories just by looking at the lengths of the rows.

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Organizing Data in Rows: Pictographs are organized into a grid format. The labels (like names of days, fruits, or students) are listed vertically on the left, and the corresponding icons are laid out horizontally to the right of each label.

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Choosing a Scale: When creating a pictograph, choosing an appropriate scale is vital. If the data values are 100,200, and 300100, 200, \text{ and } 300, a scale of 1 symbol=1001 \text{ symbol} = 100 is better than 1 symbol=21 \text{ symbol} = 2, as it keeps the graph compact and easy to read.

📐Formulae

Value of a Category=Number of full symbols×Value of one symbol\text{Value of a Category} = \text{Number of full symbols} \times \text{Value of one symbol}

Number of Symbols to draw=Total QuantityValue of one symbol\text{Number of Symbols to draw} = \frac{\text{Total Quantity}}{\text{Value of one symbol}}

Value of half symbol=12×Value of one symbol\text{Value of half symbol} = \frac{1}{2} \times \text{Value of one symbol}

💡Examples

Problem 1:

A pictograph shows the number of cars sold by a showroom in four months. The key is 1 car icon=10 cars1 \text{ car icon} = 10 \text{ cars}. In May, there are 33 full car icons and 11 half-car icon. How many cars were sold in May?

Solution:

Step 1: Identify the value of one full icon from the key, which is 10 cars10 \text{ cars}. Step 2: Calculate the value of the half-car icon: 12×10=5 cars\frac{1}{2} \times 10 = 5 \text{ cars}. Step 3: Multiply the number of full icons by the scale: 3×10=30 cars3 \times 10 = 30 \text{ cars}. Step 4: Add the value of the half icon to the total: 30+5=35 cars30 + 5 = 35 \text{ cars}.

Explanation:

To find the total value, we interpret the full symbols first and then add the fractional part represented by the partial symbol based on the given scale.

Problem 2:

A gardener planted 4545 Rose plants, 3030 Lily plants, and 2525 Jasmine plants. If we want to represent this data in a pictograph using the scale 1 flower icon=10 plants1 \text{ flower icon} = 10 \text{ plants}, how many icons should be drawn for each type?

Solution:

Step 1: For Roses, divide the total by the scale: 4510=4.5\frac{45}{10} = 4.5. This means 44 full icons and 11 half icon. Step 2: For Lilies, divide the total by the scale: 3010=3\frac{30}{10} = 3 full icons. Step 3: For Jasmine, divide the total by the scale: 2510=2.5\frac{25}{10} = 2.5. This means 22 full icons and 11 half icon.

Explanation:

To determine the number of icons needed, we divide the actual data value by the value assigned to one symbol in the key. Fractional results are represented by partial icons.