Circle graphs and central angles

Learning Objectives Identify and define the key components of a circle graph, including sectors and central angles. Calculate the percentage represented by a specific category within a dataset. Calculate the central angle corresponding to a given percentage or fraction of a whole. Construct a circle graph from a given set of data, accurately representing proportions with central angles. Interpret and extract information from existing circle graphs, relating sector sizes to data values. Explain the relationship between a part-to-whole ratio, its percentage, and its corresponding central angle in a circle graph. Ever wonder how companies show what people like most or how governments allocate funds? 📊 Imagine you want to display how your classmates spend their free time – how...

TermDefinitionExample Circle Graph (Pie Chart)A graph that uses a circle divided into sectors to show how parts relate to a whole. Each sector represents a category of data, and its size is proportional to the quantity it represents.A circle graph showing how students travel to school might have sectors for 'bus,' 'car,' 'walk,' and 'bike,' with the largest sector indicating the most common method. SectorA region of a circle bounded by two radii and the arc connecting their endpoints. In a circle graph, each sector represents a specific category of data.If a circle graph shows favorite fruits, the 'apple' slice is a sector, defined by two lines from the center of the circle to the edge, and the curved part of the circle between them. Centr...

Calculating Central Angle from Proportion $\text{Central Angle} = \frac{\text{Part}}{\text{Whole}} \times 360^\circ$ Use this rule to find the degree measure of a sector's central angle when you know the count for a specific category and the total count for all categories. The fraction 'Part/Whole' represents the proportion of the category. Calculating Central Angle from Percentage $\text{Central Angle} = \frac{\text{Percentage}}{100} \times 360^\circ$ Apply this rule when you are given the percentage for a category and need to find its corresponding central angle. Remember to convert the percentage to a decimal or fraction by dividing by 100. Sum of Central Angles $\sum \text{Central Angles} = 360^\circ$ This rule states that the sum of all central an...