To find the class boundaries of the second class, we need to analyze the intervals given in the frequency table. Class boundaries determine the real limits of each class interval. Let's go through the steps to find both the lower and upper class boundaries for the second class.
1. Understand the given class limits:
- The first class interval is [tex]\(0-10\)[/tex].
- The second class interval is [tex]\(11-21\)[/tex].
- The third class interval is [tex]\(22-32\)[/tex].
2. Determine class limits:
- For the first class, the upper class limit is [tex]\(10\)[/tex].
- For the second class, the lower class limit is [tex]\(11\)[/tex] and the upper class limit is [tex]\(21\)[/tex].
- For the third class, the lower class limit is [tex]\(22\)[/tex].
3. Calculate the lower class boundary of the second class:
The lower class boundary is typically halfway between the upper limit of the first class and the lower limit of the second class.
[tex]\[
\text{Lower class boundary of the second class} = \frac{\text{Upper class limit of the first class} + \text{Lower class limit of the second class}}{2}
\][/tex]
Substituting the values:
[tex]\[
\text{Lower class boundary of the second class} = \frac{10 + 11}{2} = \frac{21}{2} = 10.5
\][/tex]
4. Calculate the upper class boundary of the second class:
The upper class boundary is typically halfway between the upper limit of the second class and the lower limit of the third class.
[tex]\[
\text{Upper class boundary of the second class} = \frac{\text{Upper class limit of the second class} + \text{Lower class limit of the third class}}{2}
\][/tex]
Substituting the values:
[tex]\[
\text{Upper class boundary of the second class} = \frac{21 + 22}{2} = \frac{43}{2} = 21.5
\][/tex]
5. Summary:
- The lower class boundary of the second class is [tex]\(10.5\)[/tex].
- The upper class boundary of the second class is [tex]\(21.5\)[/tex].
Therefore, the class boundaries for the second class are [tex]\(10.5\)[/tex] and [tex]\(21.5\)[/tex].
