Certainly! Let's analyze the given data and construct the relative frequency distribution for each blood type.
First, we need to count the occurrences of each blood type in the sample. The given data includes 50 samples. Below, the provided blood types are categorized:
```
O, O, A, O, O
B, O, B, A, O
A B, A B, A, B, B
A, O, A, A, O
A B, O, A, A B, A
O, A, A, O, O
O, A, O, B, A
O, A B, A, A B, O
O, A, O, O, A
O, A, A, A, O
```
Count occurrences for each blood type:
- A: [tex]\(20\)[/tex] occurrences
- A B: [tex]\(6\)[/tex] occurrences
- B: [tex]\(5\)[/tex] occurrences
- O: [tex]\(18\)[/tex] occurrences
Next, compute the total number of samples, which is [tex]\(50\)[/tex].
We now calculate the relative frequency for each blood type by dividing the individual counts by the total number of samples.
Relative frequency calculation:
1. A:
[tex]\[
\text{Relative Frequency of A} = \frac{\text{Number of A samples}}{\text{Total samples}} = \frac{20}{50} = 0.4
\][/tex]
2. A B:
[tex]\[
\text{Relative Frequency of AB} = \frac{\text{Number of AB samples}}{\text{Total samples}} = \frac{6}{50} = 0.12
\][/tex]
3. B:
[tex]\[
\text{Relative Frequency of B} = \frac{\text{Number of B samples}}{\text{Total samples}} = \frac{5}{50} = 0.1
\][/tex]
4. O:
[tex]\[
\text{Relative Frequency of O} = \frac{\text{Number of O samples}}{\text{Total samples}} = \frac{18}{50} = 0.36
\][/tex]
Constructing the relative frequency distribution table:
[tex]\[
\begin{array}{|c|c|}
\hline \text{Blood Type} & \text{Relative Frequency} \\
\hline \text{A} & 0.4 \\
\hline \text{AB} & 0.12 \\
\hline \text{B} & 0.1 \\
\hline \text{O} & 0.36 \\
\hline
\end{array}
\][/tex]
So, the relative frequency distribution is:
- A: 0.40
- AB: 0.12
- B: 0.10
- O: 0.36
These calculations summarize the overall distribution of blood types within the 50 samples.
