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Data Handling - Collecting and Recording Data

Grade 3ICSE

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

🔑Concepts

What is Data: Data is a collection of information gathered by counting, measuring, or observing. It can be represented in the form of numbers, names, or symbols.

Recording Data using Tally Marks: Tally marks are a quick way of recording and counting data in groups of 55. We draw four vertical lines and the fifth line is drawn diagonally across the four lines to form a 'bundle'. Visually, 11 is |, 22 is ||, 33 is |||, 44 is ||||, and 55 is represented by four vertical sticks with a cross-bar.

Data Tables: A table is an organized arrangement of data in rows and columns. It usually has a title and headings to show what information is being recorded. Visualizing a table is like looking at a grid where the first column lists items and the next columns show their counts or tallies.

Pictographs: A pictograph is a way of representing data using pictures or symbols. For example, if we are counting apples, we might use a small drawing of an apple to represent a certain quantity.

The Key in a Pictograph: The 'Key' is the most important part of a pictograph as it tells us the value of one symbol. For instance, the key might state that 1 star symbol=10 students1 \text{ star symbol} = 10 \text{ students}. If the key is not followed, the data will be read incorrectly.

Interpreting Data: This involves looking at the recorded data to answer questions like 'Which item is the most popular?' or 'How many more items are in group A than group B?'

Observation and Collection: Before recording, data must be collected. This can be done by looking at a picture, conducting a small survey among friends, or counting objects in a room.

📐Formulae

Total Value=Number of symbols in pictograph×Value of one symbol (Key)\text{Total Value} = \text{Number of symbols in pictograph} \times \text{Value of one symbol (Key)}

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}}

Difference=Highest ValueLowest Value\text{Difference} = \text{Highest Value} - \text{Lowest Value}

💡Examples

Problem 1:

In a class, students were asked about their favorite fruit. 1414 students chose Apple, 66 students chose Mango, and 99 students chose Banana. Represent this data using Tally Marks in a table.

Solution:

Step 1: Create a table with three columns: Fruit Name, Tally Marks, and Number of Students. Step 2: For Apple (1414), draw two bundles of 55 and 44 single lines: |||| with a slash, |||| with a slash, and ||||. Step 3: For Mango (66), draw one bundle of 55 and 11 single line: |||| with a slash and |. Step 4: For Banana (99), draw one bundle of 55 and 44 single lines: |||| with a slash and ||||.

Explanation:

We group the counts into fives to make them easier to read. 1414 is 5+5+45 + 5 + 4, 66 is 5+15 + 1, and 99 is 5+45 + 4.

Problem 2:

A pictograph shows the number of cars sold by a showroom. The Key is: 1 Car Symbol=5 Cars1 \text{ Car Symbol} = 5 \text{ Cars}. If there are 44 symbols next to 'Monday' and 66 symbols next to 'Tuesday', how many total cars were sold on both days?

Solution:

Step 1: Calculate cars sold on Monday. Monday=4 symbols×5=20 cars\text{Monday} = 4 \text{ symbols} \times 5 = 20 \text{ cars}. Step 2: Calculate cars sold on Tuesday. Tuesday=6 symbols×5=30 cars\text{Tuesday} = 6 \text{ symbols} \times 5 = 30 \text{ cars}. Step 3: Find the total. Total=20+30=50 cars\text{Total} = 20 + 30 = 50 \text{ cars}.

Explanation:

To find the actual number of items in a pictograph, we multiply the number of symbols by the value given in the Key.