construct a frequency distribution and a relative - frequency histogram for the data set using five classes…

Explanation:

Step1: Find the range

The smallest value in the data - set is 1 and the largest is 10. Range = Max - Min = 10 - 1=9.

Step2: Determine the class width

We want 5 classes. Class width $w=\lceil\frac{Range}{Number\ of\ classes}\rceil=\lceil\frac{9}{5}\rceil = 2$.

Step3: Define the classes

The classes will be 1 - 2, 3 - 4, 5 - 6, 7 - 8, 9 - 10.

Step4: Count the frequencies

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

Class	Frequency
1 - 2	7
3 - 4	10
5 - 6	11
7 - 8	2
9 - 10	6

Step5: Calculate relative frequencies

Relative frequency of a class $=\frac{Frequency\ of\ the\ class}{Total\ frequency}$. Total frequency = 7 + 10+11 + 2+6=36. For the class 1 - 2: Relative frequency $=\frac{7}{36}\approx0.194$. For the class 3 - 4: Relative frequency $=\frac{10}{36}\approx0.278$. For the class 5 - 6: Relative frequency $=\frac{11}{36}\approx0.306$. For the class 7 - 8: Relative frequency $=\frac{2}{36}\approx0.056$. For the class 9 - 10: Relative frequency $=\frac{6}{36}\approx0.167$.

The class with the greatest relative frequency is 5 - 6 and the class with the least relative frequency is 7 - 8.

Answer:

Class	Frequency
1 - 2	7
3 - 4	10
5 - 6	11
7 - 8	2
9 - 10	6
The class with the greatest relative frequency is 5 - 6. The class with the least relative frequency is 7 - 8.