To construct a frequency distribution using the given data and 8 classes (0-7), we need to determine how many data points fall into each class or bin. Here’s a step-by-step guide to solving this:
1. Define the classes or bins: In this case, the classes range from 0 to 7. Each class will include integers within its range.
- Class 0: [0, 1)
- Class 1: [1, 2)
- Class 2: [2, 3)
- Class 3: [3, 4)
- Class 4: [4, 5)
- Class 5: [5, 6)
- Class 6: [6, 7)
- Class 7: [7, 8)
2. Collect the data: The given data set is:
```
[1, 2, 3, 4, 5, 6, 7, 0, 7, 5, 4, 3, 2, 1, 0, 0, 7, 6, 5, 4, 3, 2, 1, 0, 7, 7, 5, 4, 3, 2, 1, 0, 0]
```
3. Sort the data into the respective bins:
- Count how many data points fall into each bin (0-7).
4. Calculate the frequency for each class:
- Class 0: 6 data points [0, 0, 0, 0, 0, 0]
- Class 1: 4 data points [1, 1, 1, 1]
- Class 2: 4 data points [2, 2, 2, 2]
- Class 3: 4 data points [3, 3, 3, 3]
- Class 4: 4 data points [4, 4, 4, 4]
- Class 5: 4 data points [5, 5, 5, 5]
- Class 6: 2 data points [6, 6]
- Class 7: 5 data points [7, 7, 7, 7, 7]
So, the frequency distribution looks as follows:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Class} & \text{Frequency} \\
\hline
0 & 6 \\
1 & 4 \\
2 & 4 \\
3 & 4 \\
4 & 4 \\
5 & 4 \\
6 & 2 \\
7 & 5 \\
\hline
\end{array}
\][/tex]
This table summarizes the frequency distribution for each class from 0 to 7.
