Question

a frequency table of grades has five classes (a, b, c, d, f) with frequencies of 5, 14, 18, 6, and 1 respectively. using percentages, what are the relative frequencies of the five classes? complete the table. grade frequency relative frequency a 5 % b 14 % c 18 % d 6 % f 1 % (round to two decimal places as needed.)

Explanation:

Step1: Calculate total frequency

The total frequency is the sum of all individual frequencies. So, $5 + 14+18 + 6+1=44$.

Step2: Calculate relative frequency for grade A

The relative - frequency formula is $\text{Relative Frequency}=\frac{\text{Frequency}}{\text{Total Frequency}}\times100\%$. For grade A, with frequency $f_A = 5$, the relative frequency is $\frac{5}{44}\times100\%\approx11.36\%$.

Step3: Calculate relative frequency for grade B

For grade B, with frequency $f_B = 14$, the relative frequency is $\frac{14}{44}\times100\%\approx31.82\%$.

Step4: Calculate relative frequency for grade C

For grade C, with frequency $f_C = 18$, the relative frequency is $\frac{18}{44}\times100\%\approx40.91\%$.

Step5: Calculate relative frequency for grade D

For grade D, with frequency $f_D = 6$, the relative frequency is $\frac{6}{44}\times100\%\approx13.64\%$.

Step6: Calculate relative frequency for grade F

For grade F, with frequency $f_F = 1$, the relative frequency is $\frac{1}{44}\times100\%\approx2.27\%$.

Answer:

A. 11.36%, B. 31.82%, C. 40.91%, D. 13.64%, F. 2.27%