https://file.aiquickdraw.com/mathbot/file/1729229126557dv715qdv.jpg

Let's analyze the information provided:

### Frequency Table:
The frequency table was completed correctly based on the data from the responses:

- **1 meeting per quarter:** 12 responses
- **2 meetings per quarter:** 14 responses
- **3 meetings per quarter:** 18 responses
- **4 meetings per quarter:** 16 responses

### Statistical Analysis:
The questions asked for the mode, median, mean, and standard deviation.

#### Given answers:
- **Mode:** 3 (correct, as it appears most frequently, 18 times)
- **Median:** 3 (correct, since the middle values in the sorted data are both 3)
- **Mean:** 2.63 (correct, calculated by \(\frac{(1 \times 12) + (2 \times 14) + (3 \times 18) + (4 \times 16)}{60} = 2.63\))

#### Standard Deviation:
The calculated standard deviation was **1.08**, but it was marked incorrect. Let’s re-calculate it to check for any errors.

To find the standard deviation (\(\sigma\)), we can use the formula:
\[
\sigma = \sqrt{\frac{\sum (x_i - \mu)^2 \cdot f_i}{N}}
\]
where:
- \(x_i\) are the data values (1, 2, 3, 4),
- \(\mu\) is the mean (2.63),
- \(f_i\) are the frequencies (12, 14, 18, 16),
- \(N\) is the total number of responses (60).

**Calculation**:
1. Calculate \((x_i - \mu)^2\) for each \(x_i\):
   - For \(x_1 = 1\): \((1 - 2.63)^2 = 2.6569\)
   - For \(x_2 = 2\): \((2 - 2.63)^2 = 0.3969\)
   - For \(x_3 = 3\): \((3 - 2.63)^2 = 0.1369\)
   - For \(x_4 = 4\): \((4 - 2.63)^2 = 1.8769\)

2. Multiply by the corresponding frequencies and sum:
   \[
   \sum = (2.6569 \cdot 12) + (0.3969 \cdot 14) + (0.1369 \cdot 18) + (1.8769 \cdot 16)
   \]

3. Divide by \(N = 60\) and take the square root.

Let's perform the calculation to verify the correct standard deviation.The re-calculated standard deviation is approximately **1.08**, which matches the answer you provided. Therefore, the original answer appears to be correct, and it might have been marked incorrect by mistake.

### Do you have any further questions or need more details?

### Related Questions:
1. How do you calculate the variance from the standard deviation?
2. What is the importance of the mode in data analysis?
3. How can you interpret the mean if the data set is skewed?
4. What would happen to the mean and standard deviation if a new response of "4" was added?
5. How can you determine if a data set is normally distributed?

### Tip:
When calculating standard deviation, ensure you are using the correct formula (population vs. sample) as this can affect the result, especially for small data sets.

A survey was conducted to determine how often the board should meet per quarter. Residents provided responses with values between 1 and 4. The task is to fill in the frequency table and calculate the mode, median, mean, and standard deviation of the data set.

This example demonstrates how to fill in a frequency table based on survey data and calculate the mode, median, mean, and standard deviation. The data comes from a survey on how often a board should meet per quarter, with response values ranging from 1 to 4.

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