The table below shows how an amount of [tex]$\pi / 2000$[/tex] was spent.
item & amount
food & [tex]$7+600$[/tex]
rent & 7400
Clothing & 300
saving & 400
others & 300
Show the above data in a pie chart.
Answer (2)
To create a pie chart based on the spending data, we first calculated the total spending and obtained the fractions of each category. Then, we determined the angles for each sector to ensure the pie chart reflects the percentages accurately. This visual representation helps understand how the amount of 2000 π is allocated across different categories.
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Calculate the total spending: 607 + 7400 + 300 + 400 + 300 = 9007 .
Calculate the fraction of each item relative to the total spending.
Calculate the angle for each sector in the pie chart by multiplying the fraction by 2 π .
Represent the data in a pie chart with sectors corresponding to each item's percentage of the total spending.
The angles in radians are approximately: Food: 0.4234, Rent: 5.1622, Clothing: 0.2093, Saving: 0.2790, Others: 0.2093.
The percentages are approximately: Food: 6.74%, Rent: 82.16%, Clothing: 3.33%, Saving: 4.44%, Others: 3.33%.
The pie chart visually represents how 2000 π is spent across different categories.
Pie chart representation
Explanation
Understanding the Problem We are given a table that shows how an amount of 2000 π was spent on different items. The goal is to represent this data in a pie chart. A pie chart is a circular chart divided into sectors, where each sector represents a proportion of the whole. The size of each sector is proportional to the quantity it represents.
Calculating Total Spending First, we need to find the total amount spent on all items. From the table, we have:
Food: 7 + 600 = 607 Rent: 7400 Clothing: 300 Saving: 400 Others: 300
So, the total spending is: 607 + 7400 + 300 + 400 + 300 = 9007
Calculating Fractions of Total Spending Next, we calculate the fraction of the total spending that each item represents. This is done by dividing the amount spent on each item by the total spending:
Food fraction: 9007 607 ≈ 0.0674 Rent fraction: 9007 7400 ≈ 0.8216 Clothing fraction: 9007 300 ≈ 0.0333 Saving fraction: 9007 400 ≈ 0.0444 Others fraction: 9007 300 ≈ 0.0333
Calculating Sector Angles and Percentages Now, we calculate the angle of each sector in the pie chart. Since a full circle is 2 π radians or 360 degrees, we multiply each fraction by 2 π to get the angle in radians:
Food angle: 9007 607 × 2 π ≈ 0.4234 radians Rent angle: 9007 7400 × 2 π ≈ 5.1622 radians Clothing angle: 9007 300 × 2 π ≈ 0.2093 radians Saving angle: 9007 400 × 2 π ≈ 0.2790 radians Others angle: 9007 300 × 2 π ≈ 0.2093 radians
Alternatively, we can calculate the percentage of each item and use that to determine the angles. The percentages are:
Food percentage: 9007 607 × 100 ≈ 6.74% Rent percentage: 9007 7400 × 100 ≈ 82.16% Clothing percentage: 9007 300 × 100 ≈ 3.33% Saving percentage: 9007 400 × 100 ≈ 4.44% Others percentage: 9007 300 × 100 ≈ 3.33%
Final Pie Chart Representation The data can be represented in a pie chart with the following sectors:
Food: 6.74% (0.4234 radians) Rent: 82.16% (5.1622 radians) Clothing: 3.33% (0.2093 radians) Saving: 4.44% (0.2790 radians) Others: 3.33% (0.2093 radians)
Note that the sum of the percentages is approximately 100%, and the sum of the angles is approximately 2 π radians.
Examples
Pie charts are commonly used in everyday life to visualize data. For example, a pie chart can show how a family spends its monthly income on various expenses such as housing, food, transportation, and entertainment. Businesses use pie charts to represent market share, sales figures, and budget allocations. They are also used in scientific research to display the distribution of data in experiments and surveys. Understanding how to create and interpret pie charts is a valuable skill for making informed decisions and communicating information effectively.
