Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Transcribed Image Text:**Title: Analyzing Tie-Breaking Votes by U.S. Vice Presidents of the 20th Century**
**Introduction:**
The following data represents the number of tie-breaking votes cast by each of the 21 Vice Presidents of the United States who served during the twentieth century.
**Data Set:**
0, 0, 4, 10, 0, 2, 3, 3, 4, 1, 7, 8, 0, 4, 2, 0, 0, 1, 7, 0, 4
**Instructions:**
To better visualize and analyze this data, a histogram can be drawn. This will help to understand the distribution of tie-breaking votes among the Vice Presidents during this period.
**Steps to Create a Histogram:**
1. **Determine the Range:**
- Identify the smallest and largest number of tie-breaking votes. In this data set, the range is from 0 to 10.
2. **Choose Suitable Bin Intervals:**
- You could create bins such as 0-1, 2-3, 4-5, 6-7, 8-9, and 10 to categorize the data effectively.
3. **Tally the Frequencies:**
- Count how many data points fall into each bin. For example, count how many Vice Presidents cast 0 or 1 tie-breaking votes, and so on.
4. **Draw the Histogram:**
- On the horizontal axis, place the bin intervals.
- On the vertical axis, indicate the frequency of votes in each bin.
- Draw bars for each bin with heights corresponding to their frequencies.
**Conclusion:**
Creating a histogram from this data will allow for a straightforward comparison of the number of tie-breaking votes cast by Vice Presidents. This visualization helps in recognizing patterns, such as the frequency of Vice Presidents who didn’t cast any tie-breaking votes, those who cast a moderate number, and any outliers who cast a significantly higher number.
By analyzing the histogram, one can gain insights into how often Vice Presidents were called upon to break ties in the Senate during the twentieth century, providing a glimpse into the political landscape and the role of the Vice Presidency in this era.
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