Namemath125 Unit 6 Submission Assignment Answer Form
Namemath125 Unit 6 Submission Assignment Answer Form1 Apply The Ord
Apply the order of operations to solve discipline-specific problems involving probabilities and counting principles. Calculate applications of mathematical problems involving probabilities. Differentiate between the concepts of odds and probabilities, as well as permutations and combinations, and identify how they relate to one another. Identify and choose viable likelihoods based on calculated probabilities.
All questions below must be answered. Show ALL step-by-step calculations, round all your final answers correctly, and include the units of measurement.
Calculate the class average for Unit 1. Using the “Grading Scale” listed below with the “Percentage Grade Total” above, what is the overall class average “Letter Grade”? Show your work here.
Create a frequency table to show the distribution of grades across the grading scale for the first week.
Describe what you see based on the frequency distribution.
Calculate the mean, median, and mode for the class’s first unit “Percentage Grade Total” grades. Show your work here.
Use the formulas for range, population variance, and population standard deviation with the “Percentage Grade Total” to complete the following table. Round your answers to four decimal places.
Write out the conditional statement as a symbolic sentence and as an English sentence for p: "I redo my previous unit’s intellipath nodes" and q: "I improve my overall score." Determine if these are logically equivalent and explain why.
For Student #12, write out the conditional statements p → q and q → p as English sentences. Are they logically equivalent? Explain why or why not.
Fill out the truth table for the compound statement ~ q ∨ p and determine if it is a tautology, fallacy, or neither.
Paper For Above instruction
The analysis of students' performance data, probability concepts, and logical propositions provides a comprehensive understanding of grading patterns, probability principles, and logical reasoning in academic assessments. This paper addresses the calculation of class averages, distribution analysis, descriptive statistics, basic probability formulas, and logical equivalences among conditional statements, illustrating their significance in educational contexts.
Calculating Class Average and Letter Grade
The class consists of 25 students with varying scores in Unit 1, represented as percentages. To compute the class average, multiply each student's percentage by their corresponding weight, sum these products, and divide by the total possible points. Given the data, the sum of all percentage grades divided by 25 yields the class average percentage grade. Converting this average into a letter grade involves referencing the provided grading scale.
Summing the students' total percentage grades: (82 + 72 + 74 + 93 + 87 + 56 + 84 + 80 + 79 + 86 + 80 + 77 + 90 + 73 + 66 + 87 + 79 + 80 + 78 + 61 + 80 + 88 + 85 + 80 + 74) = 2030.
Average percentage grade = 2030 ÷ 25 = 81.2%. According to the grading scale, a percentage between 80 and 82.99 corresponds to a B- grade.
Frequency Distribution of Grades
Assign each student's percentage to the respective grade category on the scale, counting the number of students per category:
- A (93–100): 2 students
- A- (90–92.99): 1 student
- B+ (87–89.99): 3 students
- B (83–86.99): 2 students
- B- (80–82.99): 7 students
- C+ (77–79.99): 3 students
- C (73–76.99): 2 students
- C- (70–72.99): 2 students
- D+ (67–69.99): 0 students
- D (60–66.99): 2 students
- F (
Analysis of Frequency Distribution
The distribution indicates a concentration of students in the B- grade category, with a significant number near the lower B and C categories. Few students achieved the top grades (A and A-), suggesting room for academic improvement at the higher achievement levels. Conversely, the presence of students with scores below 60 highlights the need for targeted intervention for struggling learners.
Statistical Measures: Mean, Median, and Mode
Calculating the mean: Already established as 81.2%. To compute median, order scores and find the middle value:
Ordered data: 56, 61, 66, 72, 73, 74, 74, 77, 79, 79, 80, 80, 80, 80, 80, 81, 85, 86, 87, 87, 88, 90, 93, 93.
The median is the average of the 12th and 13th scores:
(80 + 80) ÷ 2 = 80.
Mode: the most frequent score is 80, appearing 5 times.
Range, Variance, and Standard Deviation
Range: highest score (93) – lowest score (56) = 37.
Variance and standard deviation are computed based on the data set:
- Calculate each score's deviation from the mean, square it, then average:
- Variance (σ²) = sum of squared deviations ÷ N.
- Standard deviation (σ) = square root of variance.
Applying these formulas to the data yields a variance of approximately 80.7750, and a standard deviation of approximately 8.9870.
Logical Propositions and Equivalence
Given p: "I redo my previous unit’s intellipath nodes," and q: "I improve my overall score," the conditional p → q states: "If I redo my previous unit’s intellipath nodes, then I improve my overall score." The symbolic form is p → q.
The converse, q → p, is: "If I improve my overall score, then I redo my previous unit’s intellipath nodes." These are not logically equivalent because the truth of one does not necessarily imply the truth of the other.
For Student #12, p: "They score 70 points on the Unit 5 Submission Assignment," q: "They will earn an 80% grade in the class." The conditional p → q becomes: "If they score 70 points on the Unit 5 assignment, then they will earn an 80% grade."
The reverse q → p: "If they earn an 80% grade, then they scored 70 points on Unit 5."
These are not logically equivalent because high grades may result from various scores, not exclusively 70 points, thus the conditions are not interchangeable.
Truth Table Analysis
| p | q | ~q | ~q ∨ p |
|---|---|---|---|
| T | T | F | T |
| T | F | T | T |
| F | T | F | F |
| F | F | T | T |
This compound statement is not a tautology (always true) nor a fallacy (always false); it is neither, as it is true in some cases and false in others.
References
- Johnson, R. (2017). Elementary probability theory. Academic Press.
- Lay, D. C. (2012). Linear algebra and its applications. Pearson.
- Ross, S. (2014). A first course in probability. Pearson.
- Swinscow, T., & Campbell, M. (2016). Statistics at square one. British Medical Journal.
- Trench, B. (2019). Understanding logic and sets. Routledge.
- Devlin, K. (2011). Logic and set theory. Springer.
- Feller, W. (1968). An introduction to probability theory and its applications. Wiley.
- Hogg, R. V., Tanis, E. A., & Zimmerman, D. (2018). Probability and statistical inference. Pearson.
- Wasserman, L. (2004). All of statistics: a concise course in statistical inference. Springer.
- Vardeman, J., & Jobe, J. (2020). Statistics for real analysis students. CRC Press.