Question

ns is taking a self - paced math class. his scores for each of the 13 quizzes during the academic year are shown below. complete the grouped relative frequency distribution for the data. (note that we are using a class width of 4.) write each relative frequency as a decimal rounded to the nearest hundredth, not as a percentage. quiz score: 83 80 74 76 74 88 82 89 85 79 75 90 81 quiz score relative frequency 72 to 75 76 to 79 80 to 83 84 to 87 88 to 91

Explanation:

Step1: Count frequencies

• For the interval 72 - 75: The scores 74, 74, 75 are in this range. So the frequency $f_1 = 3$.
• For the interval 76 - 79: The scores 76, 79 are in this range. So the frequency $f_2=2$.
• For the interval 80 - 83: The scores 80, 83, 82, 81 are in this range. So the frequency $f_3 = 4$.
• For the interval 84 - 87: There are no scores in this range. So the frequency $f_4=0$.
• For the interval 88 - 91: The scores 88, 89, 90 are in this range. So the frequency $f_5 = 3$.

Step2: Calculate total frequency

The total number of data - points $n=13$.

Step3: Calculate relative frequencies

• For the interval 72 - 75: The relative frequency $rf_1=\frac{f_1}{n}=\frac{3}{13}\approx0.23$.
• For the interval 76 - 79: The relative frequency $rf_2=\frac{f_2}{n}=\frac{2}{13}\approx0.15$.
• For the interval 80 - 83: The relative frequency $rf_3=\frac{f_3}{n}=\frac{4}{13}\approx0.31$.
• For the interval 84 - 87: The relative frequency $rf_4=\frac{f_4}{n}=\frac{0}{13}=0.00$.
• For the interval 88 - 91: The relative frequency $rf_5=\frac{f_5}{n}=\frac{3}{13}\approx0.23$.

Answer:

Quiz score	Relative frequency
76 to 79	0.15
80 to 83	0.31
84 to 87	0.00
88 to 91	0.23