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Data Handling - Data Representation (Bar Graphs, Line Graphs, Pie Charts, Pictographs)

Grade 6IB

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

🔑Concepts

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Data Collection and Tally Marks: Raw data is systematically recorded in a frequency distribution table. Tally marks are used to count occurrences, where four vertical lines are crossed by a diagonal fifth line to represent a group of 55 items, making it easy to calculate the final frequency.

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Pictographs: This is a visual representation using pictures or symbols to show data. A 'Key' is mandatory to explain what each symbol represents; for example, one icon of a book might represent 1010 actual books. Fractional symbols, such as half an icon, represent half the value indicated in the key.

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Bar Graphs: These consist of rectangular bars of equal width, where the length or height of the bar corresponds to the value or frequency of a category. In a vertical bar graph, the x-axis shows the categories and the y-axis shows the numerical values. The bars are separated by equal spaces to distinguish discrete data.

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Line Graphs: Ideal for showing trends over time, a line graph plots individual data points as dots on a coordinate plane. These dots are then connected by straight line segments. The horizontal axis usually represents time intervals (like months or years), while the vertical axis represents the measured quantity.

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Pie Charts (Circle Graphs): This represents data as sectors or 'slices' of a circle to show the relationship of parts to a whole. The entire circle represents 100%100\% or 360∘360^{\circ}, and the size of each sector is determined by its proportion of the total data set.

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Scale Selection: Choosing an appropriate scale is crucial for clarity. The scale is the ratio between the actual data values and the units on the graph's axis. For example, if data ranges from 00 to 10001000, a scale of 11 unit =100= 100 is more practical than 11 unit =1= 1.

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Interpreting Data: Analysis involves looking for the 'Mode' (the most frequent category shown by the tallest bar or largest pie slice) and identifying trends (upward or downward slopes in line graphs).

📐Formulae

Central Angle of a Sector=Value of CategoryTotal Value×360∘\text{Central Angle of a Sector} = \frac{\text{Value of Category}}{\text{Total Value}} \times 360^{\circ}

Percentage of a Sector=Value of CategoryTotal Value×100%\text{Percentage of a Sector} = \frac{\text{Value of Category}}{\text{Total Value}} \times 100\%

Value from Pictograph=Number of Symbols×Value per Symbol (Key)\text{Value from Pictograph} = \text{Number of Symbols} \times \text{Value per Symbol (Key)}

Total Frequency(n)=∑f=f1+f2+f3+...+fk\text{Total Frequency} (n) = \sum f = f_1 + f_2 + f_3 + ... + f_k

💡Examples

Problem 1:

In a survey of 6060 students, 1515 students chose 'Blue' as their favorite color. Calculate the central angle that represents 'Blue' in a pie chart.

Solution:

Step 1: Identify the given values. Category Value (Blue)=15\text{Category Value (Blue)} = 15 and Total Value=60\text{Total Value} = 60. \nStep 2: Use the pie chart formula: Angle=Category ValueTotal Value×360∘\text{Angle} = \frac{\text{Category Value}}{\text{Total Value}} \times 360^{\circ}. \nStep 3: Substitute the values: Angle=1560×360∘\text{Angle} = \frac{15}{60} \times 360^{\circ}. \nStep 4: Simplify the fraction: 1560=14\frac{15}{60} = \frac{1}{4}. \nStep 5: Calculate the final angle: 14×360∘=90∘\frac{1}{4} \times 360^{\circ} = 90^{\circ}.

Explanation:

To represent a portion of data in a pie chart, we find the fraction of the total it occupies and multiply it by the total degrees in a circle (360∘360^{\circ}).

Problem 2:

A pictograph uses a symbol of a bicycle to represent 88 bicycles sold. If a shop sells 3636 bicycles in a month, how many symbols must be drawn to represent this data?

Solution:

Step 1: Identify the Key. 1 symbol=8 bicycles1 \text{ symbol} = 8 \text{ bicycles}. \nStep 2: Determine the total sold: 36 bicycles36 \text{ bicycles}. \nStep 3: Divide the total by the key value: 368\frac{36}{8}. \nStep 4: Perform the division: 36÷8=4.536 \div 8 = 4.5. \nStep 5: Interpret the result: The representation requires 44 full bicycle symbols and 11 half-bicycle symbol.

Explanation:

To find the number of symbols for a pictograph, divide the actual frequency by the value assigned to one symbol in the key. Decimal results (like 0.50.5) are represented by drawing a partial symbol.