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Data Handling - Pictographs: Interpretation and Drawing

Grade 6ICSE

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

🔑Concepts

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A pictograph is a visual representation of data using images, icons, or symbols. Each symbol represents a specific quantity, which is defined by a 'Key' or 'Scale'. This method makes complex data easy to compare and understand at a glance.

A simple diagram showing three circles representing 30 items with a scale of 10 items per circle.
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The 'Scale' is the most critical part of a pictograph. It determines how many units of data one symbol stands for. For example, if 11 book icon =50= 50 books, then 44 icons represent 4×50=2004 \times 50 = 200 books.

Diagram showing a key where one rectangle symbol equals 5 units.
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Partial symbols are often used to represent values smaller than the scale. Usually, a half-symbol represents exactly half of the scale value. For instance, if a star represents 1010 units, a half-star represents 55 units.

Diagram comparing a full circle and a semi-circle to illustrate full and half scale values.
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Interpreting a pictograph involves multiplying the number of symbols by the scale value. Conversely, drawing a pictograph requires dividing the given data by the scale to find the number of symbols needed.

📐Formulae

Total Value=Number of Symbols×Value per Symbol\text{Total Value} = \text{Number of Symbols} \times \text{Value per Symbol}

Number of Symbols to be Drawn=Numerical Data ValueValue of One Symbol (Scale)\text{Number of Symbols to be Drawn} = \frac{\text{Numerical Data Value}}{\text{Value of One Symbol (Scale)}}

Value of Half Symbol=Scale Value2\text{Value of Half Symbol} = \frac{\text{Scale Value}}{2}

💡Examples

Problem 1:

The following data shows the number of bicycles sold by a shop in three days: Monday = 30, Tuesday = 45, Wednesday = 20. If we use the scale 1 symbol=10 bicycles1 \text{ symbol} = 10 \text{ bicycles}, how many symbols (including half symbols) must be drawn for each day?

Solution:

  1. For Monday: Number of symbols=3010=3\text{Number of symbols} = \frac{30}{10} = 3 symbols.
  2. For Tuesday: Number of symbols=4510=4.5\text{Number of symbols} = \frac{45}{10} = 4.5 symbols. This means we draw 44 full symbols and 11 half symbol.
  3. For Wednesday: Number of symbols=2010=2\text{Number of symbols} = \frac{20}{10} = 2 symbols.

Explanation:

To find the number of icons, we divide each day's total by the scale (1010). Since Tuesday has 45, which is not a multiple of 10, the remainder 5 is represented by exactly half of one symbol.

Problem 2:

A pictograph represents the number of trees in a park. The key states 1 tree icon=8 trees1 \text{ tree icon} = 8 \text{ trees}. If the row for 'Mango Trees' contains 33 full icons and 11 half icon, calculate the total number of Mango trees.

Solution:

  1. Value of 33 full icons = 3×8=243 \times 8 = 24 trees.
  2. Value of 11 half icon = 82=4\frac{8}{2} = 4 trees.
  3. Total number of trees = 24+4=2824 + 4 = 28 trees.

Explanation:

We first calculate the total value of the complete symbols and then add the value of the partial symbol, which is determined by dividing the scale value by 2.

Problem 3:

A fruit seller sold apples over three hours: Hour 1: 4040 kg, Hour 2: 2020 kg, Hour 3: 3030 kg. Draw a pictograph using the scale 1 apple icon=10 kg1 \text{ apple icon} = 10 \text{ kg}.

Pictograph showing 4 icons for Hour 1, 2 for Hour 2, and 3 for Hour 3.

Solution:

  1. Calculate symbols for Hour 1: 4010=4\frac{40}{10} = 4 symbols.
  2. Calculate symbols for Hour 2: 2010=2\frac{20}{10} = 2 symbols.
  3. Calculate symbols for Hour 3: 3010=3\frac{30}{10} = 3 symbols.

Explanation:

We divide the quantity of apples in each hour by the scale (1010) to find the number of apple icons to draw for each row.

Problem 4:

A school library uses a symbol of a square to represent 2020 books. If the 'Science' section has 22 full squares and 11 half square, find the total number of science books.

Visual representation of 2.5 squares representing books in the science section.

Solution:

Value of 2 full squares=2×20=40 books\text{Value of } 2 \text{ full squares} = 2 \times 20 = 40 \text{ books} Value of 1 half square=202=10 books\text{Value of } 1 \text{ half square} = \frac{20}{2} = 10 \text{ books} Total=40+10=50 books\text{Total} = 40 + 10 = 50 \text{ books}

Explanation:

Identify the scale (2020). Multiplied the number of full symbols by 2020. Added half the scale value for the partial symbol to get the final count.