Given the data set below, calculate the range, mean, sample variance, and sample standard deviation. Range = Mean = Variance = Standard deviation B 33, 26, 8, 43, 21, 37, 16, 18, 27
Given the data set below, calculate the range, mean, sample variance, and sample standard deviation. Range = Mean = Variance = Standard deviation B 33, 26, 8, 43, 21, 37, 16, 18, 27
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![### Data Analysis Exercise
Given the data set below, calculate the range, mean, sample variance, and sample standard deviation.
**Data Set:**
\[ 33, 26, 8, 43, 21, 37, 16, 18, 27 \]
**Formulas Needed:**
1. **Range**:
\[ \text{Range} = \text{Maximum value} - \text{Minimum value} \]
2. **Mean**:
\[ \text{Mean} = \frac{\sum \text{(all data points)}}{\text{Number of data points}} \]
3. **Sample Variance (s^2)**:
\[ s^2 = \frac{\sum (x_i - \bar{x})^2}{n-1} \]
where \( x_i \) is each individual data point, \( \bar{x} \) is the mean, and \( n \) is the number of data points.
4. **Sample Standard Deviation (s)**:
\[ s = \sqrt{s^2} \]
**Enter your results below:**
- **Range** =
- **Mean** =
- **Variance** =
- **Standard deviation** =
**Notes:**
- Ensure all calculations are rounded appropriately as per your standard practice or instructions.
- Use appropriate programming/software tools as needed for accurate results.
- Double-check for calculation errors by verifying each step.
**Graphical/Visual Representation:**
There are no graphs or diagrams provided in this image. However, in an educational setting, it might be useful to create visual aids such as:
- A histogram of the data points.
- A box plot to visualize the range, median, and interquartile range.
- A scatter plot with a line representing the mean and standard deviation.
These visuals can aid in comprehensively understanding the distribution and spread of the data set.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2ceb2d65-29b4-49d4-9830-4ba06589987b%2F31d6dec2-a0c8-40bf-b990-938c94961b5f%2Fyqus5ic_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Data Analysis Exercise
Given the data set below, calculate the range, mean, sample variance, and sample standard deviation.
**Data Set:**
\[ 33, 26, 8, 43, 21, 37, 16, 18, 27 \]
**Formulas Needed:**
1. **Range**:
\[ \text{Range} = \text{Maximum value} - \text{Minimum value} \]
2. **Mean**:
\[ \text{Mean} = \frac{\sum \text{(all data points)}}{\text{Number of data points}} \]
3. **Sample Variance (s^2)**:
\[ s^2 = \frac{\sum (x_i - \bar{x})^2}{n-1} \]
where \( x_i \) is each individual data point, \( \bar{x} \) is the mean, and \( n \) is the number of data points.
4. **Sample Standard Deviation (s)**:
\[ s = \sqrt{s^2} \]
**Enter your results below:**
- **Range** =
- **Mean** =
- **Variance** =
- **Standard deviation** =
**Notes:**
- Ensure all calculations are rounded appropriately as per your standard practice or instructions.
- Use appropriate programming/software tools as needed for accurate results.
- Double-check for calculation errors by verifying each step.
**Graphical/Visual Representation:**
There are no graphs or diagrams provided in this image. However, in an educational setting, it might be useful to create visual aids such as:
- A histogram of the data points.
- A box plot to visualize the range, median, and interquartile range.
- A scatter plot with a line representing the mean and standard deviation.
These visuals can aid in comprehensively understanding the distribution and spread of the data set.
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