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7. University students were surveyed and asked how many hours, h, they worked below. Hours per month, h Frequency Cumulative frequency 0

7. University students were surveyed and asked how many hours, h, they worked below. Hours per month, h Frequency Cumulative frequency 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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how many students work 40 or more hours in a month?
**Survey of University Students' Monthly Working Hours** **University students were surveyed and asked how many hours (\(h\)) they worked each month. The results are presented below.** | Hours per month, \(h\) | Frequency | Cumulative frequency | | --- | --- | --- | | \(0 < h \le 10\) | 3 | 3 | | \(10 < h \le 20\) | 7 | 10 | | \(20 < h \le 30\) | 10 | 20 | | \(30 < h \le 40\) | 14 | 34 | | \(40 < h \le 50\) | \(p\) | 44 | | \(50 < h \le 60\) | 6 | 50 | | \(60 < h \le 70\) | 4 | 54 | | \(70 < h \le 80\) | 2 | \(q\) | ### Problem: **a. Solve for \(p\) and \(q\).** - From the table, we know: - \(p + 34 = 44\) - Therefore, \(p = 44 - 34 = 10\). - The cumulative frequency for \(q\) is: - \(q = 54 + 2 = 56\). Thus, \(p = 10\) and \(q = 56\). ### CF Curve Diagram: **The first 5 class intervals in the table have been used to draw a cumulative frequency (CF) curve.** ### Explanation of the Graph: 1. **Axes:** - **x-axis:** Represents the hours per month (\(h\)). - **y-axis:** Represents the cumulative frequency. 2. **Plotting Points:** - The cumulative frequency for each class interval is plotted as follows: - \(0 < h \le 10\), frequency = 3, cumulative frequency = 3. - \(10 < h \le 20\), frequency = 7, cumulative frequency = 10. - \(20 < h \le 30\), frequency = 10, cumulative frequency = 20. - \(30 < h \le 40\), frequency = 14, cumulative frequency = 34. - \(40 < h \le 50
Transcribed Image Text:**Survey of University Students' Monthly Working Hours** **University students were surveyed and asked how many hours (\(h\)) they worked each month. The results are presented below.** | Hours per month, \(h\) | Frequency | Cumulative frequency | | --- | --- | --- | | \(0 < h \le 10\) | 3 | 3 | | \(10 < h \le 20\) | 7 | 10 | | \(20 < h \le 30\) | 10 | 20 | | \(30 < h \le 40\) | 14 | 34 | | \(40 < h \le 50\) | \(p\) | 44 | | \(50 < h \le 60\) | 6 | 50 | | \(60 < h \le 70\) | 4 | 54 | | \(70 < h \le 80\) | 2 | \(q\) | ### Problem: **a. Solve for \(p\) and \(q\).** - From the table, we know: - \(p + 34 = 44\) - Therefore, \(p = 44 - 34 = 10\). - The cumulative frequency for \(q\) is: - \(q = 54 + 2 = 56\). Thus, \(p = 10\) and \(q = 56\). ### CF Curve Diagram: **The first 5 class intervals in the table have been used to draw a cumulative frequency (CF) curve.** ### Explanation of the Graph: 1. **Axes:** - **x-axis:** Represents the hours per month (\(h\)). - **y-axis:** Represents the cumulative frequency. 2. **Plotting Points:** - The cumulative frequency for each class interval is plotted as follows: - \(0 < h \le 10\), frequency = 3, cumulative frequency = 3. - \(10 < h \le 20\), frequency = 7, cumulative frequency = 10. - \(20 < h \le 30\), frequency = 10, cumulative frequency = 20. - \(30 < h \le 40\), frequency = 14, cumulative frequency = 34. - \(40 < h \le 50
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