Question

a profess cords the following final grades in one course. construct a frequency table for the gra
a a a b b b b b b b b c
c c c c c c c 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 8 33.3 % 19
d 4 16.7 % 23
f □ □% □

Explanation:

Step1: Calculate the total number of grades

Count the number of each grade: \(3\) (A's) \(+ 8\) (B's) \(+ 8\) (C's) \(+ 4\) (D's) \(+x\) (F's). The total number of data points \(n=3 + 8+8 + 4+x\). From the cumulative frequency of D (\(23\)), and since cumulative frequency of F is cumulative frequency of D plus frequency of F. Also, by counting the original data (A:3, B:8, C:8, D:4, F:1). So frequency of F is \(1\).

Step2: Calculate the relative frequency of F

The formula for relative frequency \(rf=\frac{\text{Frequency}}{\text{Total number of data points}}\times100\%\). Total number of data points \(n = 3+8 + 8+4 + 1=24\). Relative frequency of F: \(rf=\frac{1}{24}\times100\%\approx4.2\%\)

Step3: Calculate the cumulative frequency of F

Cumulative frequency of F is cumulative frequency of D (\(23\)) plus frequency of F (\(1\)), so \(23 + 1=24\)

Answer:

Grade	Frequency	Relative frequency	Cumulative frequency
B	8	33.3%	11
C	8	33.3%	19
D	4	16.7%	23
F	1	4.2%	24