An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Calculate the percentage of each height group: 0.5%, 14%, 26.5%, 33.5%.
Verify that the percentages do not add up to 100%: 0.5 + 14 + 26.5 + 33.5 = 74.5% .
Conclude that a pie chart is not appropriate because the percentages do not represent a whole.
Determine that a bar graph is appropriate because it can display the frequencies of each height group.
Explanation
Analyze the problem We are given a table showing the frequency of college athletes' heights in different intervals. We need to determine whether a bar graph and/or a pie chart are appropriate displays for this data.
Calculate percentages for each height group First, let's calculate the percentage of athletes in each height group. This will help us determine if a pie chart is appropriate.
60-64 inches: 200 1 × 100 = 0.5%
65-69 inches: 200 28 × 100 = 14%
70-74 inches: 200 53 × 100 = 26.5%
74-76 inches: 200 67 × 100 = 33.5%
Check if percentages add up to 100% Now, let's check if these percentages add up to 100%:
0.5 + 14 + 26.5 + 33.5 = 74.5%
Determine appropriateness of bar graph and pie chart Since the percentages do not add up to 100%, a pie chart is not an appropriate display for this data. Pie charts are used to represent proportions of a whole, and the whole must be 100%.
A bar graph is appropriate for displaying the frequencies of different categories. In this case, the categories are the height intervals, and the frequencies are the number of athletes in each interval. The heights of the bars would represent the frequencies, and since we have the frequencies, a bar graph is suitable.
Conclusion Based on our analysis:
A bar graph is an appropriate display because the frequencies are given.
A pie chart is not appropriate because the categories do not add to 100%.
Examples
Imagine you're a sports analyst presenting data on player heights to a team. Using a bar graph, you can easily show the distribution of heights across different ranges, helping the coach understand the team's composition at a glance. However, a pie chart wouldn't be suitable here because the data doesn't represent parts of a whole; it's simply the count of players in each height category.
The current of 15.0 A over 30 seconds results in a total charge of 450 C . This charge corresponds to approximately 2.81 × 1 0 21 electrons flowing through the device. Therefore, a large number of electrons pass through the circuit during this time period.
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