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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 method of representing data using pictures or symbols. It provides a visual summary of information, making it easier to compare different categories at a glance.

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The 'Key' or 'Scale' is a mandatory instruction that defines the numerical value assigned to a single symbol. For example, a key might specify: 1 symbol=10 units1 \text{ symbol} = 10 \text{ units}. Visually, this is often placed in a box at the top or bottom corner of the graph.

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Consistency in Symbol Design: All symbols used in a pictograph must be of the same size and shape to ensure the visual length of the rows accurately reflects the data values. For instance, a row representing 5050 items should look exactly twice as long as a row representing 2525 items.

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Interpreting Data: To find the total value for a category, count the number of symbols and multiply it by the value given in the key. If there are 66 icons of a flower and 1 icon=5 flowers1 \text{ icon} = 5 \text{ flowers}, the total value is 6×5=306 \times 5 = 30 flowers.

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Representing Partial Symbols: When data values are not exact multiples of the scale, partial symbols are used. Visually, a half-drawn icon represents half the value of the key. For example, if 11 star represents 1010 points, then a half-star represents 55 points.

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Drawing Procedure: To construct a pictograph, first determine a suitable scale based on the common factors of the data. Then, create a table with two columns: the first for the category names (like 'Days' or 'Fruits') and the second for the corresponding number of symbols.

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Advantages of Pictographs: They are particularly useful for making large amounts of data visually appealing and easy for children or non-experts to understand without performing complex calculations.

📐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.