Question

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 testers 2 5 9 4 9 10 5 9 6 7 7 6 5 9 1 3 10 3 4 5 4 5 5 2 4 10 2 10 4 3 5 6 2 10 3 2 class □ - □ has the greatest relative frequency. (type whole numbers. use ascending order.) class □ - □ has the least relative frequency. (type whole numbers. use ascending order.)

Explanation:

Step1: Determine class - intervals

The data ranges from 1 to 10. Using 5 classes, the class - width is $\frac{10 - 1}{5}=2$. The classes are 1 - 2, 3 - 4, 5 - 6, 7 - 8, 9 - 10.

Step2: Count frequencies

For the class 1 - 2: Count the number of 1s and 2s in the data set. There are 7 values.
For the class 3 - 4: Count the number of 3s and 4s. There are 9 values.
For the class 5 - 6: Count the number of 5s and 6s. There are 11 values.
For the class 7 - 8: Count the number of 7s and 8s. There are 4 values.
For the class 9 - 10: Count the number of 9s and 10s. There are 5 values.

Step3: Calculate relative frequencies

The total number of data points $n = 36$.
Relative frequency of class 1 - 2: $\frac{7}{36}\approx0.194$.
Relative frequency of class 3 - 4: $\frac{9}{36}=0.25$.
Relative frequency of class 5 - 6: $\frac{11}{36}\approx0.306$.
Relative frequency of class 7 - 8: $\frac{4}{36}\approx0.111$.
Relative frequency of class 9 - 10: $\frac{5}{36}\approx0.139$.

Answer:

Class 5 - 6 has the greatest relative frequency.
Class 7 - 8 has the least relative frequency.