Questions: A professor records the following final grades in one course. Construct a frequency table for the grades. A A A A B B B B B B B C C C C C C C C C D D F F Complete the table. (Type an integer or decimal rounded to the nearest tenth as needed.) Grade Frequency Relative frequency Cumulative frequency A 4 17.4% 4 B 7 C 8 30.4% 34.8% D 2 F 2 8.7% 8.7% Total 23 1=100% 11 19 21 23 78

A professor records the following final grades in one course. Construct a frequency table for the grades.

A A A A B B B B B B B C C C C C C C C C D D F F

Complete the table.
(Type an integer or decimal rounded to the nearest tenth as needed.)
Grade Frequency Relative frequency Cumulative frequency
A 4 17.4% 4
B 7
C 8 30.4% 34.8%
D 2
F 2 8.7% 8.7%
Total 23 1=100% 11 19 21 23 78

Transcript text: A professor records the following final grades in one course. Construct a frequency table for the grades. A A A A B B B B B B B C C C C C C C C C D D F F Complete the table. (Type an integer or decimal rounded to the nearest tenth as needed.) Grade Frequency Relative frequency Cumulative frequency A 4 $17.4 \%$ 4 B 7 C 8 $30.4 \%$ $34.8 \%$ D 2 F 2 $8.7 \%$ $8.7 \%$ Total 23 $1=100 \%$ 11 19 21 23 78

Solution

Solution Steps

To construct a frequency table for the grades, we need to count the occurrences of each grade and calculate the relative and cumulative frequencies. The relative frequency is the proportion of each grade relative to the total number of grades, expressed as a percentage. The cumulative frequency is the running total of frequencies up to the current grade.

Step 1: Count the Frequencies

We first count the occurrences of each grade in the list:

$ A: 4 $
$ B: 7 $
$ C: 9 $
$ D: 2 $
$ F: 2 $

Step 2: Calculate Total Grades

The total number of grades is calculated as: \[ \text{Total Grades} = 4 + 7 + 9 + 2 + 2 = 24 \]

Step 3: Calculate Relative Frequencies

The relative frequency for each grade is calculated using the formula: \[ \text{Relative Frequency} = \left( \frac{\text{Frequency}}{\text{Total Grades}} \right) \times 100 \] Thus, we have:

$ A: \frac{4}{24} \times 100 = 16.7\% $
$ B: \frac{7}{24} \times 100 \approx 29.2\% $
$ C: \frac{9}{24} \times 100 = 37.5\% $
$ D: \frac{2}{24} \times 100 \approx 8.3\% $
$ F: \frac{2}{24} \times 100 \approx 8.3\% $

Step 4: Calculate Cumulative Frequencies

The cumulative frequency is calculated by summing the frequencies up to each grade:

$ A: 4 $
$ B: 4 + 7 = 11 $
$ C: 11 + 9 = 20 $
$ D: 20 + 2 = 22 $
$ F: 22 + 2 = 24 $

Final Answer

The completed frequency table is as follows:

\[ \begin{array}{|c|c|c|c|} \hline \text{Grade} & \text{Frequency} & \text{Relative Frequency (\%)} & \text{Cumulative Frequency} \\ \hline A & 4 & 16.7 & 4 \\ B & 7 & 29.2 & 11 \\ C & 9 & 37.5 & 20 \\ D & 2 & 8.3 & 22 \\ F & 2 & 8.3 & 24 \\ \hline \end{array} \]

Thus, the final answer is boxed as follows: \[ \boxed{\text{Frequency Table Completed}} \]

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