Let's break down the question step-by-step and answer each part thoroughly:
### (a) Number of Classes
First, to find the number of classes in the given data,
- The given data table has speed intervals listed as follows:
1. [tex]\(10-13.9\)[/tex]
2. [tex]\(14-17.9\)[/tex]
3. [tex]\(18-21.9\)[/tex]
4. [tex]\(22-25.9\)[/tex]
5. [tex]\(26-29.9\)[/tex]
6. [tex]\(30-33.9\)[/tex]
Count each interval:
There are 6 intervals in the table.
Thus, the number of classes is:
[tex]\[ \boxed{6} \][/tex]
### (b) Class Limits for the First Class
#### Lower Class Limit:
The lower class limit of the first class is the smallest value in its class.
For the interval [tex]\( 10-13.9 \)[/tex], the lower class limit is:
[tex]\[ \boxed{10.0} \][/tex]
#### Upper Class Limit:
The upper class limit of the first class is the largest value in its class.
For the interval [tex]\( 10-13.9 \)[/tex], the upper class limit is:
[tex]\[ \boxed{13.9} \][/tex]
### (c) Class Width
The class width is calculated by finding the difference between the lower limits (or the upper limits) of two consecutive classes. Let's determine the class width from the given data:
Take two consecutive classes:
- First class: [tex]\(10-13.9\)[/tex]
- Second class: [tex]\(14-17.9\)[/tex]
Calculate the width:
[tex]\[ 14 - 10 = 4 \][/tex]
Therefore, the class width is:
[tex]\[ \boxed{4} \][/tex]
### Summary:
(a) The number of classes is:
[tex]\[ \boxed{6} \][/tex]
(b) The lower class limit for the first class is:
[tex]\[ \boxed{10.0} \][/tex]
The upper class limit for the first class is:
[tex]\[ \boxed{13.9} \][/tex]
(c) The class width is:
[tex]\[ \boxed{4} \][/tex]
