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Sagot :
Sure, let's summarize the data by calculating the frequency, relative frequency, and percent frequency for each bin. Here is the step-by-step solution:
1. Data Description:
The data consists of 8 rows with 5 columns each, forming a table. The values represent some quantitative data point, which we will classify into different bins.
2. Bins and their Frequency:
We need to categorize the data into the following bins:
- 12-14
- 15-17
- 18-20
- 21-23
- 24-26
3. Flattening the data:
First, we'll consider all values in the data set, ignoring the structure of the table. So, we simply list all the values in a single list:
```
[14, 21, 23, 21, 16, 19, 22, 25, 16, 16, 24, 24, 25, 19, 16, 19, 18, 19, 21, 12, 16, 17, 18, 23, 25, 20, 23, 16, 20, 19, 24, 26, 15, 22, 24, 20, 22, 24, 22, 20]
```
4. Counting frequencies:
- For the bin 12-14: 2 values (12, 14)
- For the bin 15-17: 8 values (16, 16, 16, 16, 17, 15)
- For the bin 18-20: 11 values (19, 19, 18, 19, 19, 18, 20, 19, 20, 20)
- For the bin 21-23: 10 values (21, 23, 21, 22, 21, 23, 22, 22, 22, 21)
- For the bin 24-26: 9 values (25, 24, 24, 25, 25, 24, 26, 24, 24)
5. Total data points:
There are 40 data points in total.
6. Relative Frequency: (Frequency / Total Data Points)
- For the bin 12-14: [tex]\( \frac{2}{40} = 0.05 \)[/tex]
- For the bin 15-17: [tex]\( \frac{8}{40} = 0.20 \)[/tex]
- For the bin 18-20: [tex]\( \frac{11}{40} = 0.275 \)[/tex]
- For the bin 21-23: [tex]\( \frac{10}{40} = 0.25 \)[/tex]
- For the bin 24-26: [tex]\( \frac{9}{40} = 0.225 \)[/tex]
7. Percent Frequency: (Relative Frequency * 100)
- For the bin 12-14: [tex]\(0.05 \times 100 = 5.0\% \)[/tex]
- For the bin 15-17: [tex]\(0.20 \times 100 = 20.0\% \)[/tex]
- For the bin 18-20: [tex]\(0.275 \times 100 = 27.5\% \)[/tex]
- For the bin 21-23: [tex]\(0.25 \times 100 = 25.0\% \)[/tex]
- For the bin 24-26: [tex]\(0.225 \times 100 = 22.5\% \)[/tex]
So, we can now fill in the frequencies, relative frequencies, and percent frequencies:
[tex]\[ \begin{array}{l|l|l} \text{Bin} & \text{Relative Frequency} & \text{Percent Frequency (\%)} \\ \hline 12-14 & 0.05 & 5.0 \\ 15-17 & 0.20 & 20.0 \\ 18-20 & 0.275 & 27.5 \\ 21-23 & 0.25 & 25.0 \\ 24-26 & 0.225 & 22.5 \\ \end{array} \][/tex]
1. Data Description:
The data consists of 8 rows with 5 columns each, forming a table. The values represent some quantitative data point, which we will classify into different bins.
2. Bins and their Frequency:
We need to categorize the data into the following bins:
- 12-14
- 15-17
- 18-20
- 21-23
- 24-26
3. Flattening the data:
First, we'll consider all values in the data set, ignoring the structure of the table. So, we simply list all the values in a single list:
```
[14, 21, 23, 21, 16, 19, 22, 25, 16, 16, 24, 24, 25, 19, 16, 19, 18, 19, 21, 12, 16, 17, 18, 23, 25, 20, 23, 16, 20, 19, 24, 26, 15, 22, 24, 20, 22, 24, 22, 20]
```
4. Counting frequencies:
- For the bin 12-14: 2 values (12, 14)
- For the bin 15-17: 8 values (16, 16, 16, 16, 17, 15)
- For the bin 18-20: 11 values (19, 19, 18, 19, 19, 18, 20, 19, 20, 20)
- For the bin 21-23: 10 values (21, 23, 21, 22, 21, 23, 22, 22, 22, 21)
- For the bin 24-26: 9 values (25, 24, 24, 25, 25, 24, 26, 24, 24)
5. Total data points:
There are 40 data points in total.
6. Relative Frequency: (Frequency / Total Data Points)
- For the bin 12-14: [tex]\( \frac{2}{40} = 0.05 \)[/tex]
- For the bin 15-17: [tex]\( \frac{8}{40} = 0.20 \)[/tex]
- For the bin 18-20: [tex]\( \frac{11}{40} = 0.275 \)[/tex]
- For the bin 21-23: [tex]\( \frac{10}{40} = 0.25 \)[/tex]
- For the bin 24-26: [tex]\( \frac{9}{40} = 0.225 \)[/tex]
7. Percent Frequency: (Relative Frequency * 100)
- For the bin 12-14: [tex]\(0.05 \times 100 = 5.0\% \)[/tex]
- For the bin 15-17: [tex]\(0.20 \times 100 = 20.0\% \)[/tex]
- For the bin 18-20: [tex]\(0.275 \times 100 = 27.5\% \)[/tex]
- For the bin 21-23: [tex]\(0.25 \times 100 = 25.0\% \)[/tex]
- For the bin 24-26: [tex]\(0.225 \times 100 = 22.5\% \)[/tex]
So, we can now fill in the frequencies, relative frequencies, and percent frequencies:
[tex]\[ \begin{array}{l|l|l} \text{Bin} & \text{Relative Frequency} & \text{Percent Frequency (\%)} \\ \hline 12-14 & 0.05 & 5.0 \\ 15-17 & 0.20 & 20.0 \\ 18-20 & 0.275 & 27.5 \\ 21-23 & 0.25 & 25.0 \\ 24-26 & 0.225 & 22.5 \\ \end{array} \][/tex]
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