Answer :
To determine if the manager made any mistakes in drawing the pie chart, we first need to calculate the total number of tickets and the percentage each type represents. Let’s go through the process step-by-step.
1. Total Number of Tickets Sold:
We are given the following numbers for each type of ticket:
- Senior: 42
- Adult: 10
- Student: 6
- Child: 14
Sum these values to get the total number of tickets sold:
[tex]\[ 42 + 10 + 6 + 14 = 72 \][/tex]
2. Percentage of Each Type of Ticket:
Calculate the percentage of total tickets each type represents. This is done by taking the number of tickets of each type, divided by the total number of tickets, and then multiplying by 100.
- Senior tickets:
[tex]\[ \left(\frac{42}{72}\right) \times 100 = 58.333333\% \approx 58.33\% \][/tex]
- Adult tickets:
[tex]\[ \left(\frac{10}{72}\right) \times 100 = 13.888889\% \approx 13.89\% \][/tex]
- Student tickets:
[tex]\[ \left(\frac{6}{72}\right) \times 100 = 8.333333\% \approx 8.33\% \][/tex]
- Child tickets:
[tex]\[ \left(\frac{14}{72}\right) \times 100 = 19.444444\% \approx 19.44\% \][/tex]
3. Total Percentage:
The sum of these percentages should be 100%:
[tex]\[ 58.333333 + 13.888889 + 8.333333 + 19.444444 = 100.0 \][/tex]
These values and the total being exactly 100% indicate there are no computational errors in calculating the percentages.
Possible Mistakes in the Pie Chart:
Given our calculations, if the pie chart was drawn correctly, each segment should correspond proportionally to the percentages above. Here are common mistakes the manager might have made:
1. Incorrect segment size:
If the manager did not use these exact percentages, the segments would not accurately represent the data. For example, an incorrect percentage value for any of the ticket types would lead to a misrepresentation.
2. Rounding errors:
If the percentages were improperly rounded, this could lead to a total percentage not equal to 100%. Even though small rounding differences usually do not affect the pie chart significantly, the total should still sum to about 100%.
3. Labeling errors:
Even if the segments are correct in size, incorrect labeling of the segments can lead to confusion.
4. Color coding/Presentation:
If colors or other distinguishing features are incorrectly represented or inconsistently labeled in the legend, it could lead to misinterpretation.
Based on our calculations and the provided numerical result, the manager should ensure that each segment of the pie chart accurately represents the calculated percentages:
- Senior: 58.33%
- Adult: 13.89%
- Student: 8.33%
- Child: 19.44%
If these values were not used or represented correctly in the pie chart, these would be the mistakes.
1. Total Number of Tickets Sold:
We are given the following numbers for each type of ticket:
- Senior: 42
- Adult: 10
- Student: 6
- Child: 14
Sum these values to get the total number of tickets sold:
[tex]\[ 42 + 10 + 6 + 14 = 72 \][/tex]
2. Percentage of Each Type of Ticket:
Calculate the percentage of total tickets each type represents. This is done by taking the number of tickets of each type, divided by the total number of tickets, and then multiplying by 100.
- Senior tickets:
[tex]\[ \left(\frac{42}{72}\right) \times 100 = 58.333333\% \approx 58.33\% \][/tex]
- Adult tickets:
[tex]\[ \left(\frac{10}{72}\right) \times 100 = 13.888889\% \approx 13.89\% \][/tex]
- Student tickets:
[tex]\[ \left(\frac{6}{72}\right) \times 100 = 8.333333\% \approx 8.33\% \][/tex]
- Child tickets:
[tex]\[ \left(\frac{14}{72}\right) \times 100 = 19.444444\% \approx 19.44\% \][/tex]
3. Total Percentage:
The sum of these percentages should be 100%:
[tex]\[ 58.333333 + 13.888889 + 8.333333 + 19.444444 = 100.0 \][/tex]
These values and the total being exactly 100% indicate there are no computational errors in calculating the percentages.
Possible Mistakes in the Pie Chart:
Given our calculations, if the pie chart was drawn correctly, each segment should correspond proportionally to the percentages above. Here are common mistakes the manager might have made:
1. Incorrect segment size:
If the manager did not use these exact percentages, the segments would not accurately represent the data. For example, an incorrect percentage value for any of the ticket types would lead to a misrepresentation.
2. Rounding errors:
If the percentages were improperly rounded, this could lead to a total percentage not equal to 100%. Even though small rounding differences usually do not affect the pie chart significantly, the total should still sum to about 100%.
3. Labeling errors:
Even if the segments are correct in size, incorrect labeling of the segments can lead to confusion.
4. Color coding/Presentation:
If colors or other distinguishing features are incorrectly represented or inconsistently labeled in the legend, it could lead to misinterpretation.
Based on our calculations and the provided numerical result, the manager should ensure that each segment of the pie chart accurately represents the calculated percentages:
- Senior: 58.33%
- Adult: 13.89%
- Student: 8.33%
- Child: 19.44%
If these values were not used or represented correctly in the pie chart, these would be the mistakes.
