Answer :
To create a frequency distribution and calculate the relative frequency for each score from the provided data, follow these steps:
1. Listing Scores:
The provided scores are as follows:
```
[
1, 5, 8, 10, 10, 13,
3, 6, 9, 10, 11, 13,
3, 7, 9, 10, 12, 14,
4, 7, 10, 10, 12, 14
]
```
2. Calculate the Frequency:
We count how many times each score appears in the list:
- Score 1 appears 1 time.
- Score 3 appears 2 times.
- Score 4 appears 1 time.
- Score 5 appears 1 time.
- Score 6 appears 1 time.
- Score 7 appears 2 times.
- Score 8 appears 1 time.
- Score 9 appears 2 times.
- Score 10 appears 6 times.
- Score 11 appears 1 time.
- Score 12 appears 2 times.
- Score 13 appears 2 times.
- Score 14 appears 2 times.
3. Total Scores Calculation:
The total number of scores is the sum of all frequencies:
[tex]\( 1 + 2 + 1 + 1 + 1 + 2 + 1 + 2 + 6 + 1 + 2 + 2 + 2 = 24 \)[/tex]
4. Calculate the Relative Frequency:
The relative frequency is calculated by dividing the frequency of each score by the total number of scores and then multiplying by 100 to convert it to a percentage.
- For Score 1: [tex]\(\frac{1}{24} \times 100 \approx 4.2\%\)[/tex]
- For Score 3: [tex]\(\frac{2}{24} \times 100 \approx 8.3\%\)[/tex]
- For Score 4: [tex]\(\frac{1}{24} \times 100 \approx 4.2\%\)[/tex]
- For Score 5: [tex]\(\frac{1}{24} \times 100 \approx 4.2\%\)[/tex]
- For Score 6: [tex]\(\frac{1}{24} \times 100 \approx 4.2\%\)[/tex]
- For Score 7: [tex]\(\frac{2}{24} \times 100 \approx 8.3\%\)[/tex]
- For Score 8: [tex]\(\frac{1}{24} \times 100 \approx 4.2\%\)[/tex]
- For Score 9: [tex]\(\frac{2}{24} \times 100 \approx 8.3\%\)[/tex]
- For Score 10: [tex]\(\frac{6}{24} \times 100 = 25.0\%\)[/tex]
- For Score 11: [tex]\(\frac{1}{24} \times 100 \approx 4.2\%\)[/tex]
- For Score 12: [tex]\(\frac{2}{24} \times 100 \approx 8.3\%\)[/tex]
- For Score 13: [tex]\(\frac{2}{24} \times 100 \approx 8.3\%\)[/tex]
- For Score 14: [tex]\(\frac{2}{24} \times 100 \approx 8.3\%\)[/tex]
5. Create the Frequency Distribution Table:
Now we compile all this information into the table:
```
\begin{tabular}{|c|c|c|}
\hline
Score & Frequency & Relative Frequency \\
\hline
1 & 1 & 4.2\% \\
\hline
3 & 2 & 8.3\% \\
\hline
4 & 1 & 4.2\% \\
\hline
5 & 1 & 4.2\% \\
\hline
6 & 1 & 4.2\% \\
\hline
7 & 2 & 8.3\% \\
\hline
8 & 1 & 4.2\% \\
\hline
9 & 2 & 8.3\% \\
\hline
10 & 6 & 25.0\% \\
\hline
11 & 1 & 4.2\% \\
\hline
12 & 2 & 8.3\% \\
\hline
13 & 2 & 8.3\% \\
\hline
14 & 2 & 8.3\% \\
\hline
Total & 24 & \\
\hline
\end{tabular}
```
This table shows the frequency of each score and their relative frequencies rounded to the nearest tenth.
1. Listing Scores:
The provided scores are as follows:
```
[
1, 5, 8, 10, 10, 13,
3, 6, 9, 10, 11, 13,
3, 7, 9, 10, 12, 14,
4, 7, 10, 10, 12, 14
]
```
2. Calculate the Frequency:
We count how many times each score appears in the list:
- Score 1 appears 1 time.
- Score 3 appears 2 times.
- Score 4 appears 1 time.
- Score 5 appears 1 time.
- Score 6 appears 1 time.
- Score 7 appears 2 times.
- Score 8 appears 1 time.
- Score 9 appears 2 times.
- Score 10 appears 6 times.
- Score 11 appears 1 time.
- Score 12 appears 2 times.
- Score 13 appears 2 times.
- Score 14 appears 2 times.
3. Total Scores Calculation:
The total number of scores is the sum of all frequencies:
[tex]\( 1 + 2 + 1 + 1 + 1 + 2 + 1 + 2 + 6 + 1 + 2 + 2 + 2 = 24 \)[/tex]
4. Calculate the Relative Frequency:
The relative frequency is calculated by dividing the frequency of each score by the total number of scores and then multiplying by 100 to convert it to a percentage.
- For Score 1: [tex]\(\frac{1}{24} \times 100 \approx 4.2\%\)[/tex]
- For Score 3: [tex]\(\frac{2}{24} \times 100 \approx 8.3\%\)[/tex]
- For Score 4: [tex]\(\frac{1}{24} \times 100 \approx 4.2\%\)[/tex]
- For Score 5: [tex]\(\frac{1}{24} \times 100 \approx 4.2\%\)[/tex]
- For Score 6: [tex]\(\frac{1}{24} \times 100 \approx 4.2\%\)[/tex]
- For Score 7: [tex]\(\frac{2}{24} \times 100 \approx 8.3\%\)[/tex]
- For Score 8: [tex]\(\frac{1}{24} \times 100 \approx 4.2\%\)[/tex]
- For Score 9: [tex]\(\frac{2}{24} \times 100 \approx 8.3\%\)[/tex]
- For Score 10: [tex]\(\frac{6}{24} \times 100 = 25.0\%\)[/tex]
- For Score 11: [tex]\(\frac{1}{24} \times 100 \approx 4.2\%\)[/tex]
- For Score 12: [tex]\(\frac{2}{24} \times 100 \approx 8.3\%\)[/tex]
- For Score 13: [tex]\(\frac{2}{24} \times 100 \approx 8.3\%\)[/tex]
- For Score 14: [tex]\(\frac{2}{24} \times 100 \approx 8.3\%\)[/tex]
5. Create the Frequency Distribution Table:
Now we compile all this information into the table:
```
\begin{tabular}{|c|c|c|}
\hline
Score & Frequency & Relative Frequency \\
\hline
1 & 1 & 4.2\% \\
\hline
3 & 2 & 8.3\% \\
\hline
4 & 1 & 4.2\% \\
\hline
5 & 1 & 4.2\% \\
\hline
6 & 1 & 4.2\% \\
\hline
7 & 2 & 8.3\% \\
\hline
8 & 1 & 4.2\% \\
\hline
9 & 2 & 8.3\% \\
\hline
10 & 6 & 25.0\% \\
\hline
11 & 1 & 4.2\% \\
\hline
12 & 2 & 8.3\% \\
\hline
13 & 2 & 8.3\% \\
\hline
14 & 2 & 8.3\% \\
\hline
Total & 24 & \\
\hline
\end{tabular}
```
This table shows the frequency of each score and their relative frequencies rounded to the nearest tenth.
