You've been elected to the board, and to gather some information, you send out a survey to all residents about how often they think the board should meet each quarter. You get the following 60 responses:
3 2 1 2 3 2 3 2 4 1 1 3 4 3 4
3 3 2 1 1 4 3 4 4 1 4 4 4 2 3
2 3 3 3 3 3 4 4 1 3 1 1 3 1 3
1 1 3 1 2 2 1 1 1 2 2 2 2 3 4
**Mean (¯¯¯X) =**
*Round your answer to 2 decimal places as needed.*
**Standard deviation (S) =**
*Round your answer to 2 decimal places as needed.*
**c) Determine the range of variation: (¯¯¯X−S,¯¯¯X+S) =**
*Round your answers to 2 decimal places as needed.*
**d) Calculate what percent of the data values are within one standard deviation of the mean.**
*Hint: Create a histogram on paper and shade the included region(s) on your histogram to help visualize the shaded area and help with calculations.*
**Total area of shaded region =**
*Round your answer to 2 decimal places as needed.*
**Percent of area within one standard deviation =**
*Round your answer to 2 decimal places as needed.*

Let's break down the results:

**a) Mean (X̄):**  
The mean value of the responses is approximately **2.41**.

**b) Standard deviation (S):**  
The standard deviation is approximately **1.10**.

**c) Range of variation (X̄−S, X̄+S):**  
The range of variation, calculated as one standard deviation below and above the mean, is approximately **(1.31, 3.51)**.

**d) Percent of data values within one standard deviation of the mean:**  
Approximately **52.38%** of the data values fall within one standard deviation of the mean.

Would you like more details or have any questions?  
Here are some related questions to explore:

1. How does changing the sample size affect the mean and standard deviation?
2. What does it mean when a data set has a large standard deviation?
3. How could you calculate the variance from the standard deviation?
4. What is the difference between population and sample standard deviation?
5. How can you interpret the 68-95-99.7 rule for normal distributions?

**Tip:** When calculating standard deviation, remember that using the sample formula (with n-1) is appropriate when working with data from a subset rather than a whole population.

You've been elected to the board, and to gather some information, you send out a survey to all residents about how often they think the board should meet each quarter. You get the following 60 responses: 3 2 1 2 3 2 3 2 4 1 1 3 4 3 4 3 3 2 1 1 4 3 4 4 1 4 4 4 2 3 2 3 3 3 3 3 4 4 1 3 1 1 3 1 3 1 1 3 1 2 2 1 1 1 2 2 2 2 3 4. Mean (X̄) = Round your answer to 2 decimal places as needed. Standard deviation (S) = Round your answer to 2 decimal places as needed. c) Determine the range of variation: (X̄−S, X̄+S) = Round your answers to 2 decimal places as needed. d) Calculate what percent of the data values are within one standard deviation of the mean.

Learn how to calculate the mean (2.41), standard deviation (1.10), and range of variation (1.31, 3.51) for a dataset of 60 survey responses. This problem demonstrates key concepts in statistics, such as the empirical rule and measures of central tendency, suitable for Grades 9-12.

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