Sure, let’s go through the solution step-by-step. We are given the daily calorie intake data for dieters and need to fill in the values in the table, specifically focusing on calculating the relative frequency of the third class interval.
### Step-by-Step Solution:
1. Data Collection
First, let's list out the collected data on daily calorie intake:
[tex]\[
1380, 1032, 1318, 1025, 1021, 1254, 1418, 1425, 1191, 1060, 1170, 1417, 1190, 1260, 1054, 1393, 1065, 1385, 1067, 1267, 1346
\][/tex]
2. Class Intervals
We are dealing with the following class intervals:
[tex]\[
\begin{align*}
1002-1081 \\
1082-1161 \\
1162-1241 \\
1242-1321 \\
1322-1401 \\
1402-1481 \\
\end{align*}
\][/tex]
3. Frequency Calculation
We count the number of data points in each class interval.
[tex]\[
\begin{align*}
1002-1081: 7 \\
1082-1161: 0 \\
1162-1241: 3 \\
1242-1321: 4 \\
1322-1401: 4 \\
1402-1481: 3 \\
\end{align*}
\][/tex]
4. Total Data Points
The total number of data points is 21.
5. Relative Frequency Calculation
The relative frequency for the third class (1162-1241) is calculated as:
[tex]\[
\text{Relative Frequency} = \frac{\text{Frequency of Third Class}}{\text{Total Number of Data Points}}
\][/tex]
Given the frequency of the third class is 3:
[tex]\[
\text{Relative Frequency} = \frac{3}{21} = \frac{1}{7}
\][/tex]
6. Cumulative Frequency Calculation
Cumulative Frequency for each class:
[tex]\[
\begin{align*}
1002-1081: 7 \\
1082-1161: 7 \\
1162-1241: 10 \\
1242-1321: 14 \\
1322-1401: 18 \\
1402-1481: 21 \\
\end{align*}
\][/tex]
### Completed Table
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline \multicolumn{3}{|c|}{ Daily Calorie Intake for Dieters } \\
\hline Class & Frequency & Relative Frequency & Cumulative Frequency \\
\hline $1002-1081$ & 7 & & 7 \\
\hline $1082-1161$ & 0 & & 7 \\
\hline $1162-1241$ & 3 & $\frac{1}{7}$ & 10 \\
\hline $1242-1321$ & 4 & & 14 \\
\hline $1322-1401$ & 4 & & 18 \\
\hline $1402-1481$ & 3 & & 21 \\
\hline
\end{tabular}
\][/tex]
### Final Answer
The relative frequency of the third class interval (1162-1241) is [tex]\(\frac{1}{7}\)[/tex].
This completes the calculation and ensures that we have all necessary values filled in the table as required.
