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Data Handling - Pictographs

Grade 4ICSE

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

🔑Concepts

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A pictograph uses icons or pictures to represent a specific quantity of data. Each icon is linked to a 'Key' which defines its value.

Visual representation of a key in a pictograph showing a full circle as 10 units and a half circle as 5 units.
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To find the total value represented by a row, multiply the number of symbols by the value of one symbol: Total=Count×Key Value\text{Total} = \text{Count} \times \text{Key Value}

Diagram showing three boxes and a calculation indicating that 3 symbols multiplied by a key of 5 equals 15.
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When the data is not a multiple of the key, we use partial symbols. For example, if 11 symbol =4= 4 items, then 22 items are shown by a half-symbol.

Comparison of a full circle representing 4 and a semi-circle representing 2.
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The key must be chosen carefully to ensure the number of symbols to draw is manageable and fits the space provided.

📐Formulae

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

Number of Symbols to Draw=Total Data ValueValue of One Symbol\text{Number of Symbols to Draw} = \frac{\text{Total Data Value}}{\text{Value of One Symbol}}

Value of Half-Symbol=Value of One Symbol2\text{Value of Half-Symbol} = \frac{\text{Value of One Symbol}}{2}

💡Examples

Problem 1:

The following pictograph shows the number of apples sold by a shopkeeper in three days. The key says: 1 apple icon=10 kg1 \text{ apple icon} = 10 \text{ kg}. If Monday shows 44 icons and Tuesday shows 33 and a half icons, find the total kilograms of apples sold on both days.

Solution:

Step 1: Calculate apples sold on Monday. Number of icons = 44. Value per icon = 10 kg10 \text{ kg}. So, 4×10=40 kg4 \times 10 = 40 \text{ kg}. Step 2: Calculate apples sold on Tuesday. Number of icons = 3.53.5 (3 full and 1 half). Value of half-icon = 10÷2=5 kg10 \div 2 = 5 \text{ kg}. So, (3×10)+5=30+5=35 kg(3 \times 10) + 5 = 30 + 5 = 35 \text{ kg}. Step 3: Find the total. 40 kg+35 kg=75 kg40 \text{ kg} + 35 \text{ kg} = 75 \text{ kg}.

Explanation:

We use the key to convert the visual icons into numerical values by multiplying the number of icons by the weight each icon represents, ensuring we treat the half-icon as half the weight.

Problem 2:

A class has 3232 students who like Chocolate ice cream and 2424 students who like Vanilla. If we draw a pictograph where 1 star symbol=8 students1 \text{ star symbol} = 8 \text{ students}, how many stars must be drawn for each flavor?

Solution:

Step 1: Calculate stars for Chocolate. Total students=32\text{Total students} = 32. Key = 88. Number of stars = 32÷8=432 \div 8 = 4 stars. Step 2: Calculate stars for Vanilla. Total students=24\text{Total students} = 24. Key = 88. Number of stars = 24÷8=324 \div 8 = 3 stars.

Explanation:

To determine how many symbols to draw, we divide the total quantity of data for each category by the value assigned to one symbol in the key.

Problem 3:

The following pictograph shows the number of books read by four friends in a month. If each book icon represents 55 books, find the total number of books read by Rahul and Sneha combined.

Pictograph showing Rahul with 3 icons and Sneha with 4 icons.

Solution:

Rahul’s books=3×5=15\text{Rahul's books} = 3 \times 5 = 15 Sneha’s books=4×5=20\text{Sneha's books} = 4 \times 5 = 20 Combined Total=15+20=35\text{Combined Total} = 15 + 20 = 35

Explanation:

Rahul has 33 book icons next to his name. Since each icon equals 55 books, he read 1515 books. Sneha has 44 icons, so she read 2020 books. Adding them together gives 3535.

Problem 4:

A flower shop sold 4040 roses on Monday and 2525 roses on Tuesday. Represent this data in a pictograph using the key: 1 flower icon=10 roses1 \text{ flower icon} = 10 \text{ roses}. How many full and half icons are needed for Tuesday?

Pictograph showing 4 circles for Monday and 2.5 circles for Tuesday.

Solution:

Monday: 4010=4 full icons\text{Monday: } \frac{40}{10} = 4 \text{ full icons} Tuesday: 2510=2.5 icons\text{Tuesday: } \frac{25}{10} = 2.5 \text{ icons} Tuesday Icons=2 full icons and 1 half icon\text{Tuesday Icons} = 2 \text{ full icons and } 1 \text{ half icon}

Explanation:

Since 11 icon equals 1010 roses, we divide the total roses by 1010. For Tuesday, 25÷1025 \div 10 gives 22 with a remainder of 55. Since 55 is half of 1010, we draw two full flowers and one half flower.