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Smart Charts - Tally Marks

Grade 5CBSE

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

🔑Concepts

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Data Collection: Data is a collection of information, such as numbers, words, or measurements, gathered through observation or counting. In Smart Charts, we organize this data into tables using tally marks to make it easier to read and analyze.

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Tally Marks Representation: Tally marks are a visual way of representing numbers. For the numbers 1,2,3,1, 2, 3, and 44, we draw simple vertical lines: ∣| for 11, ∣∣|| for 22, ∣∣∣||| for 33, and ∣∣∣∣|||| for 44. To represent 55, we draw a diagonal line across the four vertical lines, creating a 'bundle' that looks like a small gate or a group of sticks tied together.

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Counting in Bundles: To count large numbers quickly, we group tally marks into bundles of 55. When looking at a chart, we skip-count by 55 for every complete bundle and then add the remaining individual lines. For example, two bundles and three lines are counted as 5+5+3=135 + 5 + 3 = 13.

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Frequency: Frequency is the total number of times a particular item or event occurs. In a Smart Chart, the 'Frequency' column contains the numerical value of the tally marks counted for each category.

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The Smart Chart Structure: A tally chart is usually organized into three columns. The first column lists the 'Items' or 'Categories' (e.g., types of cars, favorite fruits), the second column displays the 'Tally Marks' (the bundles and lines), and the third column displays the 'Number' or 'Frequency' (the numeric total).

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Data Analysis: Once the chart is complete, we use it to compare information. We can identify the 'Maximum' (the item with the most tally marks) and the 'Minimum' (the item with the fewest tally marks) simply by looking at which row has the longest or shortest set of tallies.

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Total Count calculation: To find the total number of items recorded in a Smart Chart, we add up all the values in the Frequency column. This represents the total size of the group or the total number of observations made.

📐Formulae

Value of one bundle=5\text{Value of one bundle} = 5

Total Frequency=∑individual frequencies\text{Total Frequency} = \sum \text{individual frequencies}

Frequency=(Number of bundles×5)+Remaining single lines\text{Frequency} = (\text{Number of bundles} \times 5) + \text{Remaining single lines}

💡Examples

Problem 1:

A group of students were asked about their favorite snacks. The responses were: Chips, Fruit, Chips, Cake, Fruit, Chips, Chips, Cake, Chips, Fruit. Create a tally mark table and find the total number of students.

Solution:

  1. Identify the categories: Chips, Fruit, Cake.
  2. Count and mark tallies:
  • Chips: 55 occurrences →\rightarrow represented as one bundle of four vertical lines and one diagonal line.
  • Fruit: 33 occurrences →\rightarrow represented as ∣∣∣|||.
  • Cake: 22 occurrences →\rightarrow represented as ∣∣||.
  1. Create the Frequency column:
  • Chips = 55
  • Fruit = 33
  • Cake = 22
  1. Calculate Total: 5+3+2=105 + 3 + 2 = 10.

Explanation:

We first list each unique snack. For every time a snack is mentioned, we put a tally mark in its row. Once we hit 55 for 'Chips', we close the bundle. Adding all frequencies gives the total number of students surveyed.

Problem 2:

In a park, Rahul saw some animals and recorded them using tally marks. For birds, he drew 33 bundles and 44 single lines. For squirrels, he drew 22 bundles. How many more birds did he see than squirrels?

Solution:

  1. Calculate the number of birds: Rahul saw 33 bundles and 44 lines. Using the formula: (3×5)+4=15+4=19(3 \times 5) + 4 = 15 + 4 = 19 birds.
  2. Calculate the number of squirrels: Rahul saw 22 bundles. Using the formula: 2×5=102 \times 5 = 10 squirrels.
  3. Find the difference: 19−10=919 - 10 = 9.

Explanation:

To solve this, we convert the visual tally descriptions into numerical frequencies using the 'bundle of 5' rule. After finding the frequency for both animals, we subtract the smaller number from the larger one to find the difference.