The part of the circle that represents each value that the variable takes.
- The angle of the sector is calculated by dividing 360 (the degrees of a complete circle) by the number of data and multiplying the result by the absolute frequency of each data.
- The formula to find these calculations is the following:
[tex]\text { Ángulo del sector }=\frac{360}{n^o \text { datos }} \times \text { frecuencia de cada dato }[/tex]
- Each sector is constructed with an angle protractor.
Answer (2)
To find the angle of each sector in a pie chart, first determine the total number of data points and the frequency for each. Use the formula θ i = n 360 × f i to calculate each sector's angle, then construct the sectors using a protractor. This method helps to visually represent data proportions effectively.
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Define the total number of data points as n and the frequency of the i -th data point as f i .
Calculate the angle θ i of each sector using the formula: θ i = n 360 × f i .
Use a protractor to construct each sector with the calculated angle θ i .
The angle of each sector represents the proportion of each value of a variable, providing a visual representation of the data. θ i = n 360 × f i
Explanation
Problem Analysis The problem explains how to calculate the angle of each sector in a pie chart. The angle of each sector represents the proportion of each value of a variable. The angle of a sector is calculated by dividing 360 degrees by the total number of data points and multiplying the result by the frequency of each data point. The formula for calculating the angle of a sector is: A ˊ ngulo del sector = n o datos 360 × frecuencia de cada dato . Each sector is constructed using a protractor.
Define variables Let's define the variables:
n = total number of data points
f i = frequency of the i -th data point
θ i = the angle of the i -th sector in degrees
Calculate the angle of each sector The angle of the i -th sector is calculated using the formula: θ i = n 360 × f i
Construct each sector To construct each sector, use a protractor to draw an angle of θ i degrees. Start at an arbitrary radius and measure the angle counterclockwise. The next sector starts where the previous one ended.
Examples
Pie charts are commonly used to visualize the distribution of expenses in a budget. For example, if you want to represent how you spend your monthly income, you can categorize your expenses (rent, food, transportation, entertainment, etc.) and calculate the percentage of your income spent on each category. Then, you can create a pie chart where each sector represents a different expense category, and the angle of each sector corresponds to the proportion of your income spent on that category. This allows you to quickly see where your money is going and identify areas where you can potentially save.
