Four thousand students at a school were asked to name their favorite pizza topping. The results were 800 Pepperoni, 1,000 Sausage, 1,200 Mushrooms, 560 Peppers, 240 Onions, and 200 Other. Your friend expresses these results in this circle graph. Your friend made a mistake, however. What is wrong with his graph?
A)
The numbers add up to more than 100%.
B)
The percent for Mushrooms is incorrect.
C)
All the values in the graph are incorrect.
D)
The values for Pepperoni and Peppers are reversed.
Obviously, we can't see the graph.
To determine what is wrong with your friend's graph, we need to compare the given information with the representation in the circle graph.
According to the information provided, there were 4,000 students in total who were surveyed. The results of the survey show the following favorite pizza toppings:
- Pepperoni: 800 students
- Sausage: 1,000 students
- Mushrooms: 1,200 students
- Peppers: 560 students
- Onions: 240 students
- Other: 200 students
Now, let's analyze each answer choice:
A) The numbers add up to more than 100%.
To check if the numbers add up to more than 100%, we need to convert the values into percentages.
- Pepperoni: (800/4000) * 100 = 20%
- Sausage: (1000/4000) * 100 = 25%
- Mushrooms: (1200/4000) * 100 = 30%
- Peppers: (560/4000) * 100 = 14%
- Onions: (240/4000) * 100 = 6%
- Other: (200/4000) * 100 = 5%
Adding up these percentages, we get 20 + 25 + 30 + 14 + 6 + 5 = 100%. Therefore, the numbers do not add up to more than 100%, so option A is incorrect.
B) The percent for Mushrooms is incorrect.
To check if the percentage for mushrooms is correct, we can compare the given value of 1,200 students with the actual calculated percentage of (1200/4000) * 100 = 30%. Since the given value matches the calculated percentage, option B is incorrect.
C) All the values in the graph are incorrect.
Since we have verified options A and B as incorrect, option C, stating that all the values in the graph are incorrect, is also incorrect.
D) The values for Pepperoni and Peppers are reversed.
To check this, we can compare the given values of Pepperoni (800) and Peppers (560) with their respective percentages.
- Pepperoni: (800/4000) * 100 = 20%
- Peppers: (560/4000) * 100 = 14%
Comparing the percentages, we see that Pepperoni has a higher percentage than Peppers. However, the circle graph represents Peppers with a larger slice than Pepperoni, which means the values are indeed reversed. Therefore, option D is correct, and the mistake in your friend's graph is that the values for Pepperoni and Peppers are reversed.
The correct answer is D) The values for Pepperoni and Peppers are reversed.