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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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A Line Graph is a visual way to display data that changes continuously over a period of time. It consists of several points (called markers) connected by straight line segments, which look like a zigzag or climbing line on a grid.

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The Horizontal Axis (X-axis) and Vertical Axis (Y-axis) form the structure of a graph. The X-axis usually represents the independent variable, like time (days, months, or hours), while the Y-axis represents the quantity being measured (like temperature or height). They meet at the origin, usually labeled 00.

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Interpreting trends in a line graph involves looking at the direction of the line. If the line moves upwards from left to right, it shows an 'increase'. If it moves downwards, it shows a 'decrease'. A horizontal flat line indicates no change over that period.

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A Pie Chart is a circular graph used to show how a whole is divided into parts or fractions. Visually, it looks like a pizza or a pie divided into different sized slices, known as 'sectors'.

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In a Pie Chart, the size of each sector is proportional to the quantity it represents. This means a larger quantity will have a wider 'slice' with a larger central angle, while a smaller quantity will have a narrower slice.

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Every Pie Chart must account for the whole set of data. This means that if you add up the percentages of every sector, they must equal 100%100\%. If you add up the angles of the sectors around the center point, they must equal 360∘360^{\circ}.

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A Key or Legend is a small box next to the graph or chart that explains what the different colors or line styles represent. For example, in a pie chart showing favorite fruits, the key might show that 'Red' represents 'Apples' and 'Yellow' represents 'Bananas'.

📐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.