Sure, let's work through the problem step-by-step.
We have been given a dataset that represents scores or values arranged in a grid:
[tex]\[
\begin{array}{llllllllll}
6 & 4 & 2 & 4 & 3 & 2 & 9 & 5 & 4 & 4 \\
3 & 3 & 2 & 2 & 9 & 3 & 5 & 4 & 0 & 2 \\
3 & 3 & 4 & 4 & 5 & 3 & 4 & 2 & 2 \\
4 & 3 & 4 & 4 & 3 & 3 & 3 & 3 & 3 & 2
\end{array}
\][/tex]
To solve the task, we need to:
1. Flatten the two-dimensional array into a one-dimensional list.
2. Create a frequency table.
3. Calculate the mean.
4. Calculate the median.
5. Determine the mode.
### Step 1: Flatten the List
First, we will combine all values into a single list.
[tex]\[ \text{Flattened data} = [6, 4, 2, 4, 3, 2, 9, 5, 4, 4, 3, 3, 2, 2, 9, 3, 5, 4, 0, 2, 3, 3, 4, 4, 5, 3, 4, 2, 2, 4, 3, 4, 4, 3, 3, 3, 3, 3, 2] \][/tex]
### Step 2: Frequency Table
Next, we will create a frequency table by counting the occurrences of each unique value.
| Value | Frequency |
|-------|-----------|
| 0 | 1 |
| 2 | 8 |
| 3 | 13 |
| 4 | 11 |
| 5 | 3 |
| 6 | 1 |
| 9 | 2 |
### Step 3: Calculate the Mean
To find the mean, we sum all the values in the flattened list and divide by the number of values.
[tex]\[
\text{Mean} = \frac{\sum \text{all values}}{\text{number of values}} = \frac{138}{39} \approx 3.538
\][/tex]
### Step 4: Calculate the Median
The median is the middle value in a sorted list of numbers. Since the total number of values we have is 39 (an odd number), the median is the value at the [tex]\( \frac{39+1}{2} = 20 \)[/tex]-th position of the sorted list.
[tex]\[ \text{Sorted list} = [0, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, {\bf 3}, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 6, 9, 9] \][/tex]
The 20-th value in the sorted list is 3. Hence, the median is 3.0.
### Step 5: Determine the Mode
The mode is the value with the highest frequency in the dataset.
From the frequency table, we see:
- Value 3 appears 13 times (the highest frequency).
So, the mode is 3.
### Summary
Based on the calculations:
- Frequency Table: {0: 1, 2: 8, 3: 13, 4: 11, 5: 3, 6: 1, 9: 2}
- Mean: 3.538
- Median: 3.0
- Mode: 3
