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Data Handling and Presentation - Collecting and Organising Data

Grade 6CBSE

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

🔑Concepts

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Data: A collection of numbers or facts gathered to provide specific information is called data. For example, the marks of students in a class or the temperature of a city over a week.

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Recording Data: Before processing, data must be recorded carefully. For example, recording the choices of fruits by students in a class: Apple, Banana, Apple, Orange, etc.

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Organizing Data: To make data easier to read and analyze, we use a frequency distribution table. We use Tally Marks to count the occurrences of each data point.

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Tally Marks: These are a quick way of keeping track of numbers in groups of five. A single vertical line ∣| represents 11, and a group of five is represented by four vertical lines with a diagonal line across them like this: ∣∣∣∣\cancel{||||} (or 55).

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Pictograph: A pictograph represents data through pictures of objects. It helps express a large amount of information in a visually appealing way. A Scale is used where one picture represents a certain number of items (e.g., 11 picture =10= 10 students).

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Bar Graph: A bar graph (or bar chart) is a representation of data using bars of uniform width. The heights (or lengths) of these bars are proportional to the values they represent. The spacing between the bars must be uniform.

📐Formulae

Value represented in Pictograph=Number of symbols×Value of one symbol\text{Value represented in Pictograph} = \text{Number of symbols} \times \text{Value of one symbol}

Length of a bar in Bar Graph=Numerical Value of DataScale Unit\text{Length of a bar in Bar Graph} = \frac{\text{Numerical Value of Data}}{\text{Scale Unit}}

Total Frequency=∑Individual Frequencies\text{Total Frequency} = \sum \text{Individual Frequencies}

💡Examples

Problem 1:

The following are the marks obtained by 1010 students in a math test: 7,8,5,7,6,7,8,5,5,77, 8, 5, 7, 6, 7, 8, 5, 5, 7. Organize this data using tally marks.

Solution:

We create a frequency table: MarksTally MarksNumber of Students (Frequency)5∣∣∣36∣17∣∣∣∣48∣∣2Total10\begin{array}{|c|c|c|} \hline \text{Marks} & \text{Tally Marks} & \text{Number of Students (Frequency)} \\ \hline 5 & ||| & 3 \\ 6 & | & 1 \\ 7 & |||| & 4 \\ 8 & || & 2 \\ \hline \text{Total} & & 10 \\ \hline \end{array}

Explanation:

We count how many times each mark appears. 55 appears 33 times, 66 appears 11 time, 77 appears 44 times, and 88 appears 22 times. These counts are represented by tally marks and recorded as frequency.

Problem 2:

In a pictograph, if the symbol △\triangle represents 55 cars, how many cars are represented by 6126\frac{1}{2} symbols?

Solution:

Given: 1 symbol (△)=5 cars1 \text{ symbol } (\triangle) = 5 \text{ cars}. Total symbols =6.5= 6.5. Total cars=6.5×5=32.5\text{Total cars} = 6.5 \times 5 = 32.5 Since cars cannot be in decimals in real-world count, the half symbol represents 22 or 33 cars (usually rounded). Calculated mathematically: 6×5+12×5=30+2.5=32.56 \times 5 + \frac{1}{2} \times 5 = 30 + 2.5 = 32.5

Explanation:

We multiply the number of symbols by the scale factor. A full symbol represents 55 units, and a half symbol represents half of the scale value (2.52.5).

Problem 3:

If the scale on a bar graph is 1 unit length=10 students1 \text{ unit length} = 10 \text{ students}, what is the length of the bar representing 4545 students?

Solution:

Length of bar=Total StudentsScale\text{Length of bar} = \frac{\text{Total Students}}{\text{Scale}} Length of bar=4510=4.5 units\text{Length of bar} = \frac{45}{10} = 4.5 \text{ units}

Explanation:

To find the height of the bar, divide the actual numerical value by the value represented by one unit of the scale.