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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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A pictograph is a way of representing data using pictures or icons, where each icon stands for a specific quantity called the 'Scale' or 'Key'.

Diagram showing a circle icon representing 5 students as a key for a pictograph.
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When a quantity is not a perfect multiple of the scale, partial symbols (like half an icon) are used to represent smaller values. For example, if 11 icon represents 1010 units, then half an icon represents 55 units.

Comparison of a full circle and a semi-circle showing whole and half values.
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To interpret a pictograph, we multiply the number of symbols for a category by the value of the key. Total value = (Full symbols ×\times Key) + (Partial symbols ×\times Fraction of Key).

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To draw a pictograph, we decide on a suitable scale that can represent all data points clearly without drawing too many symbols. We then divide the data value by the scale to find the number of icons needed.

📐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.

Problem 3:

The following table shows the number of books read by students in a library over three days. Draw a pictograph using the scale 1 square icon=4 books1 \text{ square icon} = 4 \text{ books}. Day 1: 1212 books Day 2: 66 books Day 3: 88 books

Pictograph showing squares for books: 3 for Day 1, 1.5 for Day 2, and 2 for Day 3.

Solution:

  1. Calculate symbols for Day 1: 124=3\frac{12}{4} = 3 squares.
  2. Calculate symbols for Day 2: 64=1\frac{6}{4} = 1 full square and 11 half square (since 22 is half of 44).
  3. Calculate symbols for Day 3: 84=2\frac{8}{4} = 2 squares.

Explanation:

We use the scale 11 square =4= 4 books. For Day 2, since 66 is not a multiple of 44, we use 11 full square (44) and half a square (22) to total 66.

Problem 4:

Look at the pictograph representing the number of fruit baskets sold by a merchant. If 1 circle icon=20 baskets1 \text{ circle icon} = 20 \text{ baskets}, find the difference in the number of baskets sold between Merchant A and Merchant B.

Pictograph with circles: Merchant A has 4 circles, Merchant B has 2.5 circles.

Solution:

  1. Merchant A has 44 full circles. Total =4×20=80= 4 \times 20 = 80 baskets.
  2. Merchant B has 22 full circles and 11 half circle. Total =(2×20)+(12×20)=40+10=50= (2 \times 20) + (\frac{1}{2} \times 20) = 40 + 10 = 50 baskets.
  3. Difference =80−50=30= 80 - 50 = 30 baskets.

Explanation:

Identify the number of icons for each person. Multiply by the scale factor of 2020. Subtract the values to find the difference.