(a) Construct a stem-and-leaf plot for the examinationgrades in which the stems are 1, 2, 3,..., 9.

1. Break Down the Problem

To construct a stem-and-leaf plot for the examination grades, we need to identify the stems and leaves properly. The stems represent the leading digit(s) (tens or higher), while the leaves represent the final digit (ones place) of each grade.

2. Relevant Concepts

• Each grade can be broken down into a stem (the first digit or first two digits) and a leaf (the last digit).
• The range of stems is from 1 to 9, which indicates that the grades to be considered are in the range of 10 to 99.

3. Details

1. Identify the Data: You need a list of examination grades. For instance, let's suppose the grades are: 12, 15, 22, 23, 35, 42, 49, 51, 67, 78, 82, 85, 91, 92, 95.
2. Organize the Data: Arrange the grades in ascending order:
   • 12, 15, 22, 23, 35, 42, 49, 51, 67, 78, 82, 85, 91, 92, 95
3. Extract Stems and Leaves:
   • Stem 1: 2 5
   • Stem 2: 2 3
   • Stem 3: 5
   • Stem 4: 2 9
   • Stem 5: 1
   • Stem 6: 7
   • Stem 7: 8
   • Stem 8: 2 5
   • Stem 9: 1 2 5

4. Verify and Summarize

Ensure all grades are included and represented accurately in the plot.

Final Answer

The stem-and-leaf plot for the given examination grades is:

Stem | Leaf
1    | 2 5
2    | 2 3
3    | 5
4    | 2 9
5    | 1
6    | 7
7    | 8
8    | 2 5
9    | 1 2 5

This representation allows for easy visualization of the distribution of grades and their frequency.