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Data Handling - Interpreting Data

Grade 3IB

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

🔑Concepts

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Data can be represented visually using Pictographs, where a symbol represents a specific quantity defined by a 'Key'. Interpreting a pictograph requires multiplying the number of symbols by the key value.

A pictograph showing circles representing ice cream sales with a key indicating each circle equals 2 units.
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Bar Graphs use rectangular bars of different heights or lengths to show and compare data. The height of the bar corresponds to a value on the scale (usually the vertical axis).

A bar graph with three bars of heights 5, 10, and 7.
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Interpreting data involves answering questions like 'Which category has the most?', 'Which has the least?', and 'What is the difference between two categories?'

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Tally Marks are a quick way to record data in groups of 55. Every fifth mark is a diagonal line across the previous four vertical marks: ∣∣∣∣|||| with a slash.

📐Formulae

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

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

Total Data Points=Sum of all Frequencies\text{Total Data Points} = \text{Sum of all Frequencies}

💡Examples

Problem 1:

In a pictograph about favorite fruits, the Key states that 1 apple icon=5 students1 \text{ apple icon} = 5 \text{ students}. If the row for 'Grapes' has 44 apple icons, how many students chose grapes as their favorite fruit?

Solution:

Step 1: Identify the number of symbols for Grapes, which is 44. Step 2: Identify the value of each symbol from the key, which is 55. Step 3: Multiply the number of symbols by the key value: 4×5=204 \times 5 = 20.

Explanation:

To find the actual value in a pictograph, you must multiply the number of pictures seen by the value each picture represents in the key.

Problem 2:

A bar graph shows that 1212 children like Dogs and 77 children like Cats. How many more children prefer Dogs than Cats?

Solution:

Step 1: Note the value for Dogs, which is 1212. Step 2: Note the value for Cats, which is 77. Step 3: Subtract the smaller number from the larger number: 12−7=512 - 7 = 5.

Explanation:

When a question asks 'how many more' or 'the difference,' we use subtraction to compare the two heights on the bar graph.

Problem 3:

Look at the pictograph of 'Books Read'. If the key is 1 Book Symbol=3 books1 \text{ Book Symbol} = 3 \text{ books}, how many books did Sarah read if she has 44 symbols next to her name?

Pictograph row for Sarah with 4 box symbols and a key of 3 books per box.

Solution:

Sarah read 1212 books.

Explanation:

According to the key, each symbol represents 33 books. Sarah has 44 symbols. Total books = 4×3=124 \times 3 = 12.

Problem 4:

A bar graph shows the number of stars collected by students. Group A has a bar reaching 1515 and Group B has a bar reaching 99. How many more stars does Group A have than Group B?

A bar graph comparing Group A (15) and Group B (9).

Solution:

66 stars.

Explanation:

To find how many more, we subtract the value of Group B from Group A: 15−9=615 - 9 = 6.