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Data Handling - Interpretation of Charts

Grade 3ICSE

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

🔑Concepts

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Data is a collection of facts, such as numbers, words, or measurements, collected to provide information. In a table, data is usually organized into rows and columns to make it easier to read.

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Tally Marks are a quick way of recording data in groups of five. We draw vertical lines for the first four items ∣∣∣∣||||, and for the fifth item, we draw a diagonal line across the four lines. This makes it easy to skip-count by 55 to find the total.

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A Pictograph is a chart that uses pictures or symbols to represent data. For example, if we are counting books, we might use a small book icon. It helps us visualize the data quantities at a glance.

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The 'Key' or 'Legend' is a crucial instruction that tells us what each symbol in a pictograph represents. If the key says 11 ball symbol =5= 5 balls, then 33 ball symbols actually represent 3×5=153 \times 5 = 15 balls.

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Bar Graphs represent data using rectangular bars. These bars can be drawn vertically (standing up) or horizontally (lying down). The height or length of the bar corresponds to the value it represents; a taller bar indicates a larger quantity.

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Interpreting charts involves looking at the labels on the axes (the bottom and side lines of a graph). The 'X-axis' usually shows the categories (like colors or names), and the 'Y-axis' shows the numbers or scale.

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Comparison of data is done by looking at the bars or symbols. We can identify the 'Most Popular' or 'Highest' category by looking for the longest bar or the most symbols, and the 'Least Popular' or 'Lowest' by looking for the shortest bar or fewest symbols.

📐Formulae

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

Difference=Greater Value−Smaller Value\text{Difference} = \text{Greater Value} - \text{Smaller Value}

Grand Total=Sum of all category values\text{Grand Total} = \text{Sum of all category values}

💡Examples

Problem 1:

In a school library pictograph, the key states that 11 book symbol =10= 10 books. If the 'Science' section has 66 book symbols and the 'History' section has 44 book symbols, how many more Science books are there than History books?

Solution:

Step 1: Calculate the number of Science books: 6×10=606 \times 10 = 60. \ Step 2: Calculate the number of History books: 4×10=404 \times 10 = 40. \ Step 3: Find the difference: 60−40=2060 - 40 = 20.

Explanation:

We first use the key to convert the symbols into actual numbers by multiplying. Then, we subtract the smaller amount from the larger amount to find the difference.

Problem 2:

A fruit seller uses tally marks to count baskets of fruit sold. The tally for Apples is a group of five and three extra lines. The tally for Oranges is two groups of five. How many baskets of fruit were sold in total?

Solution:

Step 1: Find the number of Apple baskets: 5+3=85 + 3 = 8. \ Step 2: Find the number of Orange baskets: 5+5=105 + 5 = 10. \ Step 3: Calculate the total: 8+10=188 + 10 = 18.

Explanation:

First, decode the tally marks into numbers. A bundle with a diagonal line represents 55. After finding the individual counts, add them together to get the grand total.