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Data Handling - Recording and Organisation of Data

Grade 6CBSE

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

🔑Concepts

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Data is a collection of numbers gathered to give some information. Raw data refers to data collected in its original form without any specific arrangement, such as a list of marks obtained by 1010 students.

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Recording Data is the process of noting down observations as they occur. For instance, if you are counting the types of cars passing a gate, you record each car as it passes.

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Organisation of Data involves arranging raw data in a systematic way, usually in a table, to make it easy to understand and analyze. A typical data table contains columns for the observation, tally marks, and the frequency.

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Tally Marks are used to count the occurrences of data points in groups of 55. Each observation is marked with a vertical line ∣|. When the count reaches 55, a diagonal line is drawn across the previous four lines to form a 'bundle'. For example, the number 1313 is represented by two bundles of five and three extra lines: ∣ ⁣∣ ⁣∣ ⁣∣∖|\!|\!|\!| \setminus ∣ ⁣∣ ⁣∣ ⁣∣∖|\!|\!|\!| \setminus ∣ ⁣∣ ⁣∣|\!|\!|.

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Frequency refers to the total number of times a particular observation occurs in the data set. If the number 77 appears 44 times in a list, its frequency is 44.

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A Pictograph is a way of representing data using pictures or symbols. Each symbol represents a specific number of items, which is defined in a 'scale' or 'key'. Visually, if a symbol of a basket represents 1010 fruits, then half a basket symbol might represent 55 fruits.

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A Bar Graph consists of rectangular bars (columns) of uniform width with equal spacing between them. The height or length of the bar represents the value of the data. The bars can be vertical or horizontal. For example, if 11 unit of height on the vertical axis represents 100100 people, a bar that is 33 units high represents 300300 people.

📐Formulae

Total Number of Observations=∑Frequencies\text{Total Number of Observations} = \sum \text{Frequencies}

Value of a category in Pictograph=(Number of symbols)×(Value per symbol)\text{Value of a category in Pictograph} = (\text{Number of symbols}) \times (\text{Value per symbol})

Number of symbols to draw=Total value of the categoryValue per symbol\text{Number of symbols to draw} = \frac{\text{Total value of the category}}{\text{Value per symbol}}

Actual Value in Bar Graph=(Length of bar in units)×(Scale value per unit)\text{Actual Value in Bar Graph} = (\text{Length of bar in units}) \times (\text{Scale value per unit})

💡Examples

Problem 1:

The marks obtained by 1212 students in a math test out of 1010 are: 7,8,5,7,6,8,7,9,5,7,6,87, 8, 5, 7, 6, 8, 7, 9, 5, 7, 6, 8. Organize this data in a frequency distribution table.

Solution:

We identify the unique marks and count their occurrences:\n1. Marks 55: Appears 22 times. Tally: ∣∣||, Frequency: 22.\n2. Marks 66: Appears 22 times. Tally: ∣∣||, Frequency: 22.\n3. Marks 77: Appears 44 times. Tally: ∣∣∣∣||||, Frequency: 44.\n4. Marks 88: Appears 33 times. Tally: ∣∣∣|||, Frequency: 33.\n5. Marks 99: Appears 11 time. Tally: ∣|, Frequency: 11.\nTotal frequency = 2+2+4+3+1=122+2+4+3+1 = 12.

Explanation:

The solution involves identifying distinct values (marks), recording them in ascending order, using tally marks for counting, and writing the final count as frequency.

Problem 2:

In a pictograph, one symbol of a tree represents 2020 trees. If a forest has 140140 Mango trees and 8080 Neem trees, how many symbols should be drawn for each?

Solution:

Given scale: 1 symbol=20 trees1 \text{ symbol} = 20 \text{ trees}.\nFor Mango trees: Number of symbols=14020=7\text{Number of symbols} = \frac{140}{20} = 7 symbols.\nFor Neem trees: Number of symbols=8020=4\text{Number of symbols} = \frac{80}{20} = 4 symbols.

Explanation:

To find the number of symbols for a pictograph, divide the actual quantity of the item by the value that one symbol represents.