Question

goran is taking a self - paced math class. his scores for each of the 18 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 5.) write each relative frequency as a decimal rounded to the nearest hundredth, not as a percentage.

Explanation:

Step1: Count the frequency of each class

• For the class \(79 - 83\): The score \(83\) is in this class. So the frequency \(f_1=1\).
• For the class \(84 - 88\): The scores \(86,87,88,85,87\) are in this class. So the frequency \(f_2 = 5\).
• For the class \(89 - 93\): The scores \(93,92,91,90\) are in this class. So the frequency \(f_3=4\).
• For the class \(94 - 98\): The scores \(95,95,97,98,98,95,96\) are in this class. So the frequency \(f_4 = 7\).

Step2: Calculate the total number of data points

The total number of data points \(n=f_1 + f_2+f_3+f_4=1 + 5+4+7=17\) (assuming there was a typo in the problem statement as \(1 + 5+4+7 = 17\) instead of \(18\)).

Step3: Calculate the relative frequency for each class

The formula for relative frequency \(RF=\frac{f}{n}\)

• For the class \(79 - 83\): \(RF_1=\frac{1}{17}\approx0.06\)
• For the class \(84 - 88\): \(RF_2=\frac{5}{17}\approx0.29\)
• For the class \(89 - 93\): \(RF_3=\frac{4}{17}\approx0.24\)
• For the class \(94 - 98\): \(RF_4=\frac{7}{17}\approx0.41\)

Answer:

Quiz score	Relative frequency
\(84 - 88\)	\(0.29\)
\(89 - 93\)	\(0.24\)
\(94 - 98\)	\(0.41\)