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Data Handling - Creating and Interpreting Line Graphs and Pie Charts

Grade 5IB

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

🔑Concepts

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Line graphs are used to show how a specific quantity changes over a continuous period of time. Data points are plotted and then connected by straight lines to reveal trends such as increases, decreases, or stability.

A line graph showing a series of connected points representing a trend over time.
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A Pie Chart (or Circle Graph) represents data as 'slices' of a whole circle. Each slice (sector) shows the relative size of a category compared to the total sum of all categories.

A pie chart with a highlighted 90-degree sector representing 25 percent of the total.
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The size of a sector in a pie chart is determined by the central angle. Since a full circle is 360∘360^{\circ}, a category that represents half the data will have an angle of 180∘180^{\circ}.

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When interpreting line graphs, look for the 'slope' of the lines. A line going upwards from left to right indicates an increase, while a line going downwards indicates a decrease.

📐Formulae

Angle of a Sector=Value of CategoryTotal Value×360∘\text{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\%

Total sum of internal angles=360∘\text{Total sum of internal angles} = 360^{\circ}

Total sum of percentages=100%\text{Total sum of percentages} = 100\%

💡Examples

Problem 1:

A line graph shows the temperature in a classroom recorded over three hours. At 9:009:00 AM it was 20∘C20^{\circ}C, at 10:0010:00 AM it was 24∘C24^{\circ}C, and at 11:0011:00 AM it was 22∘C22^{\circ}C. What was the change in temperature between 9:009:00 AM and 10:0010:00 AM, and what was the overall trend from 10:0010:00 AM to 11:0011:00 AM?

Solution:

Step 1: Identify the values. Temp9am=20∘CTemp_{9am} = 20^{\circ}C and Temp10am=24∘CTemp_{10am} = 24^{\circ}C. Step 2: Calculate the difference: 24∘C−20∘C=4∘C24^{\circ}C - 20^{\circ}C = 4^{\circ}C. The temperature increased by 4∘C4^{\circ}C. Step 3: Observe the trend from 10:0010:00 AM to 11:0011:00 AM. Since the value went from 24∘C24^{\circ}C to 22∘C22^{\circ}C, the line on the graph moves downwards, indicating a 'decreasing' trend.

Explanation:

To find the change, we subtract the earlier value from the later value. To identify a trend, we look at whether the line segments are sloping upwards (increase) or downwards (decrease).

Problem 2:

In a class of 2020 students, 55 students chose 'Blue' as their favorite color. If you were drawing a pie chart to represent this data, what would be the angle of the sector for 'Blue'?

Solution:

Step 1: Identify the part and the whole. Part =5= 5, Total =20= 20. Step 2: Use the formula for the sector angle: Angle=520×360∘\text{Angle} = \frac{5}{20} \times 360^{\circ}. Step 3: Simplify the fraction: 520=14\frac{5}{20} = \frac{1}{4}. Step 4: Multiply by the total degrees: 14×360∘=90∘\frac{1}{4} \times 360^{\circ} = 90^{\circ}.

Explanation:

To find the angle of a pie chart slice, we first determine what fraction of the whole the category represents, then multiply that fraction by the 360∘360^{\circ} that make up a full circle.

Problem 3:

A plant's height was measured every Monday for 4 weeks. On Week 1 it was 22 cm, Week 2 it was 55 cm, Week 3 it was 66 cm, and Week 4 it was 99 cm. Plot this data on a line graph. What was the growth between Week 1 and Week 4?

Line graph showing plant growth over 4 weeks from 2cm to 9cm.

Solution:

9 cm−2 cm=7 cm9 \text{ cm} - 2 \text{ cm} = 7 \text{ cm}

Explanation:

To find the total growth, we subtract the initial height in Week 1 (22 cm) from the final height in Week 4 (99 cm). The result is 77 cm.

Problem 4:

A surveyor asked 4040 people about their favorite fruit. 2020 people chose Apple, 1010 chose Banana, and 1010 chose Orange. Calculate the angle for the 'Apple' sector in a pie chart.

Pie chart split into one half for Apple and two quarters for Banana and Orange.

Solution:

Angle=2040×360∘=180∘\text{Angle} = \frac{20}{40} \times 360^{\circ} = 180^{\circ}

Explanation:

The 'Apple' category accounts for 2020 out of 4040 total responses, which is 12\frac{1}{2} of the total. Half of a full 360∘360^{\circ} circle is 180∘180^{\circ}.