A set of data contains a total of 130 items which are divided into six groups for display on a pie chart. If one group contains 26 items, then the sector representing this group on the pie chart contains an angle at the center of the circle that is:
A. 36
B. 60
C. 70
D. 72
Answer (2)
The angle representing the group of 26 items in the pie chart is 72 degrees. This is calculated by finding the proportion of items in the group and multiplying by 360 degrees. Therefore, the correct answer is D. 72 .
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Calculate the proportion of the group with 26 items: 130 26 .
Multiply the proportion by 360 degrees to find the angle: 130 26 × 360 .
Simplify the expression: 5 1 × 360 = 72 .
The angle at the center of the circle is: 72 .
Explanation
Problem Analysis We are given a set of data with 130 items divided into six groups for a pie chart. One group contains 26 items, and we need to find the angle at the center of the circle representing this group.
Calculating the Proportion and Angle To find the angle, we first need to determine the proportion of the group with 26 items to the total number of items. This proportion is given by: 130 26 Next, we multiply this proportion by 360 degrees (since a full circle has 360 degrees) to find the angle at the center of the circle: 130 26 × 360
Simplifying the Expression and Finding the Angle Now, let's simplify the expression: 130 26 × 360 = 5 1 × 360 = 72 So, the angle at the center of the circle representing the group with 26 items is 72 degrees.
Final Answer Therefore, the sector representing this group on the pie chart contains an angle of 72 degrees at the center of the circle.
Examples
Pie charts are commonly used to represent proportions in various real-life scenarios. For example, in a school, a pie chart can represent the proportion of students enrolled in different subjects. If a school has 130 students and 26 are enrolled in mathematics, the sector representing mathematics would have a central angle of 72 degrees, visually indicating the proportion of students studying math compared to other subjects.
