Math Problem Statement
A professor records the following final grades in one course. Construct a frequency table for the grades.
A
A
A
Upper BB
Upper BB
B
B
B
B
B
B
C C
C
C
C
C
C
Upper CC
Upper DD
D
D
Upper DD
Upper FF
Question content area bottom
Part 1
Complete the table.
(Type an integer or decimal rounded to the nearest tenth as needed.)
Grade
Frequency
Relative frequency
Cumulative frequency
A
enter your response here
enter your response here%
enter your response here
Solution
To construct the frequency table for the grades provided, we first need to tally the occurrences of each grade, then calculate the relative and cumulative frequencies.
Step 1: Count the Frequencies
- A: 3
- Upper BB: 2
- B: 6
- C: 7
- Upper CC: 1
- Upper DD: 3
- D: 2
- Upper FF: 1
Step 2: Total Count of Grades
Total grades = 3 (A) + 2 (Upper BB) + 6 (B) + 7 (C) + 1 (Upper CC) + 3 (Upper DD) + 2 (D) + 1 (Upper FF) = 25
Step 3: Calculate Relative Frequencies
Relative Frequency = (Frequency / Total Grades) × 100
Step 4: Cumulative Frequencies
Cumulative frequency is the sum of the frequencies up to and including that grade.
Frequency Table
| Grade | Frequency | Relative Frequency (%) | Cumulative Frequency |
|---|---|---|---|
| A | 3 | 12.0 | 3 |
| Upper BB | 2 | 8.0 | 5 |
| B | 6 | 24.0 | 11 |
| C | 7 | 28.0 | 18 |
| Upper CC | 1 | 4.0 | 19 |
| Upper DD | 3 | 12.0 | 22 |
| D | 2 | 8.0 | 24 |
| Upper FF | 1 | 4.0 | 25 |
Summary
- Total Grades: 25
- The relative frequencies are rounded to the nearest tenth of a percent.
Would you like to delve deeper into any part of this analysis or have specific questions? Here are some related questions for further exploration:
- How would you interpret the distribution of grades?
- What percentage of students received grades lower than a B?
- How might the grading distribution affect overall course assessments?
- What statistical measures could be applied to further analyze this data?
- How can this frequency table assist in understanding student performance?
Tip: When constructing frequency tables, ensure to double-check your counts and calculations for accuracy.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Statistics
Frequency Distribution
Relative Frequency
Cumulative Frequency
Formulas
Relative Frequency = (Frequency / Total Count) × 100
Cumulative Frequency = Sum of frequencies up to and including that grade
Theorems
-
Suitable Grade Level
Grades 10-12