Questions: Construct a frequency distribution and a relative frequency histogram for the data set using five classes. Which class has the greatest relative frequency and which has the least relative frequency? Ratings from 1 (lowest) to 10 (highest) from 36 taste tester: 1 6 9 1 10 9 5 9 7 7 5 6 9 1 4 10 4 5 4 5 6 2 3 9 10 4 3 5 5 1 8 4 Class Frequency 1-2 7 3-4 8 5-6 10 7-8 3 9-10 8 Class has the greatest relative frequency. (Type whole numbers. Use ascending order.)

Construct a frequency distribution and a relative frequency histogram for the data set using five classes. Which class has the greatest relative frequency and which has the least relative frequency? Ratings from 1 (lowest) to 10 (highest) from 36 taste tester: 1 6 9 1 10 9 5 9 7 7 5 6 9 1 4 10 4 5 4 5 6 2 3 9 10 4 3 5 5 1 8 4 Class Frequency 1-2 7 3-4 8 5-6 10 7-8 3 9-10 8 Class has the greatest relative frequency. (Type whole numbers. Use ascending order.)
Transcript text: Construct a frequency distribution and a relative frequency histogram for the data set using five classes. Which class has the greatest relative frequency and which has the least relative frequency? Ratings from 1 (lowest) to 10 (highest) from 36 taste tester: \begin{tabular}{cccccccc} 1 & 6 & 9 & 1 & 10 & 9 & 5 & 9 \\ 7 & 7 & 5 & 6 & 9 & 1 & 4 & 10 \\ 4 & 5 & 4 & 5 & 6 & 2 & 3 & 9 \\ 10 & 4 & 3 & 5 & 5 & 1 & 8 & 4 \end{tabular} \begin{tabular}{|c|c|} \hline Class & Frequency \\ \hline $1-2$ & 7 \\ $3-4$ & 8 \\ $5-6$ & 10 \\ $7-8$ & 3 \\ $9-10$ & 8 \\ \hline \end{tabular} Class $\square$ $\square$ has the greatest relative frequency. (Type whole numbers. Use ascending order.)
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Solution

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Solution Steps

Step 1: Construct the Frequency Distribution
  • The given data is divided into five classes with their respective frequencies:
    • Class 1-2: Frequency = 7
    • Class 3-4: Frequency = 8
    • Class 5-6: Frequency = 10
    • Class 7-8: Frequency = 3
    • Class 9-10: Frequency = 8
Step 2: Calculate the Relative Frequency
  • Relative frequency is calculated by dividing the frequency of each class by the total number of data points.
  • Total number of data points = 7 + 8 + 10 + 3 + 8 = 36
    • Class 1-2: Relative Frequency = 7/36 ≈ 0.194
    • Class 3-4: Relative Frequency = 8/36 ≈ 0.222
    • Class 5-6: Relative Frequency = 10/36 ≈ 0.278
    • Class 7-8: Relative Frequency = 3/36 ≈ 0.083
    • Class 9-10: Relative Frequency = 8/36 ≈ 0.222
Step 3: Identify the Greatest and Least Relative Frequencies
  • Greatest Relative Frequency: Class 5-6 (0.278)
  • Least Relative Frequency: Class 7-8 (0.083)

Final Answer

  • Class with the greatest relative frequency: 5-6
  • Class with the least relative frequency: 7-8
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