Question

a professor records the following final grades in one course. construct a frequency table for the grades.
a a a b b b b b b b b c
c c c c c c d d d d d f
complete the table.
(type an integer or decimal rounded to the nearest tenth as needed.)
grade frequency relative frequency cumulative frequency
a 3 12.5 % 3
b 8 33.3 % 11
c □ □% □

Explanation:

Step1: Count Frequency of C

Count the number of 'C's. From the grades: C, C, C, C, C, C, C (wait, original list: first C group: 3? Wait no, original grades: A (3), B (8), then C: let's recount. The grades are: A (3), B (8), then C: looking at the list: "C, C, C, C, C, C, D..." Wait the given grades: after B (8), then C: let's list all:

A: 3 (A, A, A)

B: 8 (B, B, B, B, B, B, B, B)

Then C: let's count: C, C, C, C, C, C, C? Wait the original text: "C, C, C, C, C, C, D, D, D, D, D, F" Wait no, the user's input:

Original grades:

A: 3 (A, A, A)

B: 8 (B, B, B, B, B, B, B, B)

Then C: "C, C, C, C, C, C, D, D, D, D, D, F" Wait no, the sequence is:

After B (8), the next are: C, C, C, C, C, C, D, D, D, D, D, F? Wait no, the user's text:

"A, A, A, B, B, B, B, B, B, B, B, C, C, C, C, C, C, D, D, D, D, D, F" Wait maybe I miscounted. Let's count total grades:

A: 3

B: 8 (so 3+8=11)

Then C: let's see the next grades: C, C, C, C, C, C, D, D, D, D, D, F. Wait the C's: how many? Let's count the C's:

Looking at the user's input: "C, C, C, C, C, C, D, D, D, D, D, F" Wait no, the original problem's grades:

After B (8), the grades are: C, C, C, C, C, C, D, D, D, D, D, F? Wait no, the user's text:

"A, A, A, B, B, B, B, B, B, B, B, C, C, C, C, C, C, D, D, D, D, D, F" Wait the C's: let's count:

First C: 1

Second: 2

Third: 3

Fourth: 4

Fifth: 5

Sixth: 6

Seventh: 7? Wait no, the user's input: "C, C, C, C, C, C, D, D, D, D, D, F" Wait the C's are 6? Wait no, the original problem's grades:

Wait the user's text: "A, A, A, B, B, B, B, B, B, B, B, C, C, C, C, C, C, D, D, D, D, D, F" Wait that's 3 A, 8 B, 7 C? Wait no, let's count the C's:

Looking at the sequence after B (8):

C (1), C (2), C (3), C (4), C (5), C (6), C (7)? Wait no, the user's input: "C, C, C, C, C, C, D, D, D, D, D, F" Wait the C's are 6? Wait maybe I made a mistake. Wait the total number of grades:

A: 3

B: 8 (3+8=11)

C: let's see, then D: 5, F:1. So total grades: 3+8+C+5+1 = total. Let's count all grades:

A: 3

B: 8 (3+8=11)

C:?

D: 5 (D, D, D, D, D)

F:1

So total: 3+8+C+5+1 = 17 + C. Wait the number of C's: let's count the C's in the given list:

The grades are:

A, A, A,

B, B, B, B, B, B, B, B,

C, C, C, C, C, C, C,

D, D, D, D, D,

F

Wait no, the user's input: "C, C, C, C, C, C, D, D, D, D, D, F" Wait after B (8), the next are C, C, C, C, C, C, D, D, D, D, D, F. So C's: 6? Wait no, the user's text: "C, C, C, C, C, C, D, D, D, D, D, F" – that's 6 C's? Wait no, let's count the characters:

C (1), C (2), C (3), C (4), C (5), C (6), D (1), D (2), D (3), D (4), D (5), F (1). So C: 6? Wait but then total grades: 3 (A) +8 (B)+6 (C)+5 (D)+1 (F)=23? Wait no, that can't be. Wait maybe I misread the original grades. Let's re-express the original problem's grades:

The professor's grades:

A: A, A, A (3)

B: B, B, B, B, B, B, B, B (8)

C: C, C, C, C, C, C, C (7)? Wait the user's input: "C, C, C, C, C, C, D, D, D, D, D, F" – no, the C's are 7? Wait the user's text: "C, C, C, C, C, C, D, D, D, D, D, F" – that's 6 C's? Wait no, the number of C's: let's count the C's in the list:

Looking at the user's input:

"A, A, A, B, B, B, B, B, B, B, B, C, C, C, C, C, C, D, D, D, D, D, F"

So A: 3, B: 8, C: 7? Wait no, the C's are 7? Wait the sequence after B (8) is: C (1), C (2), C (3), C (4), C (5), C (6), C (7), D (1), D (2), D (3), D (4), D (5), F (1). So C:7. Then total grades: 3+8+7+5+1=24. Wait but the relative frequency of A is 3/24=12.5%, which matches (3/24=0.125=12.5%). B:8/24≈33.3%, which also matches (8/24≈0.333). So total is 24. So C's frequency: 24 -3 (A) -8 (B) -5 (D) -1 (F) =24-17=7. So frequency of C is 7.

Step2: Calculate Relative Frequency of C

Relative frequency = (Frequency of C) / Total number of grades. Total is 24. So 7/24 ≈0.2917, which is 29.2% (rounded to nearest tenth).

Step3: Calculate Cumulative Frequency of C

Cumulative frequency is sum of frequencies of A, B, and C. So 3 (A) +8 (B) +7 (C) =18.

Answer:

Frequency of C: 7, Relative frequency: 29.2%, Cumulative frequency: 18

So the table for C:

Grade | Frequency | Relative frequency | Cumulative frequency
--- | --- | --- | ---
C | 7 | 29.2% | 18