Connect with experts and get insightful answers on IDNLearn.com. Whether your question is simple or complex, our community is here to provide detailed and trustworthy answers quickly and effectively.

For the data given below, calculate the number of children, frequency, and median:

[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]

Construct a frequency table and graph the data. Calculate the mean and median.

[tex]\[
\begin{tabular}{|c|c|}
\hline
\text{Number of Children} & \text{Frequency} \\
\hline
1 & 2 \\
\hline
2 & \\
\hline
\end{tabular}
\][/tex]


Sagot :

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