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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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A Pictograph represents data using icons or symbols. A key is essential to define the numerical value assigned to a single symbol, allowing for the calculation of total quantities through multiplication. For example, if 1 book symbol equals 55 books, then 33 symbols represent 1515 books.

Pictograph showing 3 book symbols and a key indicating 1 symbol equals 10 books.
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A Bar Graph uses rectangular bars of uniform width to compare different categories. The height (for vertical bars) or length (for horizontal bars) represents the frequency or value of each category. The axes must be labeled, and a consistent scale must be used.

A vertical bar graph comparing categories A, B, and C with different heights.
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A Pie Chart (or Circle Graph) shows the relationship of parts to a whole. The entire circle represents 100%100\% or 360∘360^{\circ}. Each sector's size is proportional to the quantity it represents, calculated using the central angle formula.

Pie chart divided into two sectors: 25 percent and 75 percent.
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A Line Graph displays information as a series of data points called 'markers' connected by straight line segments. It is primarily used to track changes or trends over periods of time (e.g., temperature over a week).

A line graph showing an upward trend with fluctuations over time.

📐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.

Problem 3:

The following table shows the marks obtained by a student in three subjects: Math (8080), Science (6060), and English (4040). Represent this data using a vertical bar graph with a scale of 11 unit = 2020 marks.

Bar graph showing Math at 80, Science at 60, and English at 40 marks.

Solution:

  1. Determine the bar heights:
  • Math: 80/20=480 / 20 = 4 units
  • Science: 60/20=360 / 20 = 3 units
  • English: 40/20=240 / 20 = 2 units
  1. Draw the xx-axis for subjects and the yy-axis for marks.
  2. Draw the bars according to the calculated units.

Explanation:

In a bar graph, the height is directly proportional to the value. Since our scale is 2020, we divide each score by 2020 to find the height in graph units.

Problem 4:

A baker sells 120120 cakes in total. The sales consist of: Chocolate (6060), Vanilla (3030), and Strawberry (3030). Create a pie chart to represent this data and find the central angle for the Chocolate sector.

Pie chart with Chocolate taking up half the circle and Vanilla and Strawberry taking up quarters.

Solution:

  1. Total Value: 120120
  2. Central Angle for Chocolate: 60120×360∘=12×360∘=180∘\frac{60}{120} \times 360^{\circ} = \frac{1}{2} \times 360^{\circ} = 180^{\circ}
  3. Central Angle for Vanilla/Strawberry: 30120×360∘=14×360∘=90∘\frac{30}{120} \times 360^{\circ} = \frac{1}{4} \times 360^{\circ} = 90^{\circ}
  4. The Chocolate sector will be a semi-circle (180∘180^{\circ}), and the others will be quarter-circles (90∘90^{\circ}).

Explanation:

The central angle represents the proportion of the total. Since Chocolate is exactly half of the total sales (6060 out of 120120), its angle is half of 360∘360^{\circ}, which is 180∘180^{\circ}.