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Smart Charts - Data Collection

Grade 3CBSE

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

🔑Concepts

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Data Collection: Data is a collection of facts, such as numbers, words, measurements, or observations. In Smart Charts, we collect information like the number of students who like a specific fruit or the number of different colored cars in a parking lot to organize it clearly.

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Tally Marks: Tally marks are a quick way of keeping track of numbers in groups of five. We draw vertical lines ∣| for each count. For the number 55, we draw four vertical lines and one diagonal line crossing through them to form a 'bundle' like this: ∣∣∣∣|||| with a slash. For example, the number 77 is shown as one bundle of 55 and two extra lines ∣∣||.

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Pictographs: A pictograph uses pictures or symbols to represent data. Every pictograph must have a 'Key' which explains what each symbol stands for. For example, if a picture of one apple represents 22 apples, then 33 apple pictures mean 3×2=63 \times 2 = 6 apples.

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Bar Charts: Bar charts represent data using rectangular bars of different heights or lengths. In a vertical bar chart, the taller the bar, the higher the value it represents. You can compare different items easily by looking at which bar is the tallest (most) and which is the shortest (least).

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Recording Data in Tables: To make sense of collected information, we use a table. A typical table has three columns: the 'Item' name, the 'Tally Marks' to count them, and the 'Number' (frequency) which is the total count of the tally marks.

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Interpreting Charts: This involves reading the chart to answer questions. For example, by looking at a chart of favorite ice cream flavors, you can find the difference between the most popular and least popular flavor by subtracting the smaller number from the larger one.

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Scaling: Sometimes, one symbol or one unit on a chart represents more than one object. This is called scaling. For example, on a bar chart, the numbers on the side might jump by 22s (0,2,4,6...0, 2, 4, 6...) or 55s (0,5,10,15...0, 5, 10, 15...) instead of 11s to save space.

📐Formulae

Total Count=Sum of all individual item counts\text{Total Count} = \text{Sum of all individual item counts}

Value of Symbols=Number of symbols×Value per symbol\text{Value of Symbols} = \text{Number of symbols} \times \text{Value per symbol}

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

💡Examples

Problem 1:

In a class, 88 students like Mango, 55 students like Apple, and 33 students like Orange. Create a Tally Mark table for this data and find the total number of students.

Solution:

  1. Create a table with three columns: Fruit, Tally Marks, and Number.
  2. For Mango: Draw 11 bundle of five and 33 lines →\rightarrow ∣∣∣∣|||| (crossed) ∣∣∣||| = 88.
  3. For Apple: Draw 11 bundle of five →\rightarrow ∣∣∣∣|||| (crossed) = 55.
  4. For Orange: Draw 33 lines →\rightarrow ∣∣∣||| = 33.
  5. Total students = 8+5+3=168 + 5 + 3 = 16.

Explanation:

We use tally marks to group the data. The bundle represents 55, making it easier to count large numbers. Adding all the frequencies gives the total population of the data set.

Problem 2:

A pictograph uses a 'Star' symbol ★\bigstar to represent 44 toys. If Rohan has 55 stars next to his name, how many toys does he have in total?

Solution:

  1. Identify the value of one symbol: 1 star=4 toys1 \text{ star} = 4 \text{ toys}.
  2. Count the number of symbols for Rohan: 5 stars5 \text{ stars}.
  3. Multiply the number of symbols by the value per symbol: 5×4=205 \times 4 = 20.
  4. Rohan has 2020 toys.

Explanation:

Using a key allows us to represent large numbers with fewer symbols. By multiplying the count of symbols by the key value, we find the actual quantity.