Question

constructing a relative frequency distribution for grouped data
kevin is taking a self - paced math class. his scores for each of the 14 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.
quiz score
91 85 83 97 90
98 80 90 93 82
91 92 81 89

Explanation:

Step1: Count the frequency of each class

• For \(79 - 83\): The scores \(83,80,82,81\) are in this class. Frequency \(f_1 = 4\)
• For \(84 - 88\): The score \(85\) is in this class. Frequency \(f_2=1\)
• For \(89 - 93\): The scores \(91,90,90,93,91,92,89\) are in this class. Frequency \(f_3 = 7\)
• For \(94 - 98\): The scores \(97,98\) are in this class. Frequency \(f_4=2\)

Step2: Calculate the total number of data points

Total number of data points \(n=f_1 + f_2+f_3 + f_4=4 + 1+7+2=14\)

Step3: Calculate the relative frequency for each class

• Relative frequency formula: \(RF=\frac{f}{n}\)
• For \(79 - 83\): \(RF_1=\frac{4}{14}\approx0.29\)
• For \(84 - 88\): \(RF_2=\frac{1}{14}\approx0.07\)
• For \(89 - 93\): \(RF_3=\frac{7}{14}=0.50\)
• For \(94 - 98\): \(RF_4=\frac{2}{14}\approx0.14\)

Answer:

Quiz score	Relative frequency
\(84 - 88\)	\(0.07\)
\(89 - 93\)	\(0.50\)
\(94 - 98\)	\(0.14\)