--- ### Consider the following sample data: - **Sample A:** 11, 22, 33 - **Sample B:** 81, 92, 103 - **Sample C:** 1,100; 1,111; 1,122 --- #### (a) Find the mean and standard deviation for each sample. | | Sample A | Sample B | Sample C | |------------------|--------------|--------------|--------------| | **Mean** | | | | | **Sample Standard Deviation** | | | | #### (b) What does this exercise show about the standard deviation? - The idea is to illustrate that the standard deviation is not a function of the value of the mean. - The idea is to illustrate that the standard deviation is a function of the value of the mean. --- *(Note: The table above requires values for the mean and sample standard deviations to be filled in by the students during the exercise.)* In this exercise, students will take the given samples and calculate the mean and standard deviation to understand the relationship between these statistical measures. --- This page is intended to help students grasp the concept of mean and standard deviation, demonstrating that the variability of data (standard deviation) does not necessarily depend on the central tendency (mean) of the data. Rather, it depends on how spread out the values are from the mean. For example, in this exercise: - Sample A consists of lower values compared to Sample B and Sample C. - Despite the differences in the value ranges, students may observe how the standard deviations compare when they are calculated. --- #### Instructions: 1. Calculate the mean for each sample by summing all the data points in the sample and dividing by the number of data points. 2. Calculate the sample standard deviation for each sample using the formula for sample standard deviation. Formula for sample standard deviation: \[ s = \sqrt{\frac{1}{N-1} \sum_{i=1}^{N} (x_i - \bar{x})^2} \] Where \( N \) is the number of observations, \( x_i \) is each individual observation, and \( \bar{x} \) is the sample mean. Complete the table and choose the correct option for part (b) based on your understanding and calculations. --- **End of Exercise** ---
--- ### Consider the following sample data: - **Sample A:** 11, 22, 33 - **Sample B:** 81, 92, 103 - **Sample C:** 1,100; 1,111; 1,122 --- #### (a) Find the mean and standard deviation for each sample. | | Sample A | Sample B | Sample C | |------------------|--------------|--------------|--------------| | **Mean** | | | | | **Sample Standard Deviation** | | | | #### (b) What does this exercise show about the standard deviation? - The idea is to illustrate that the standard deviation is not a function of the value of the mean. - The idea is to illustrate that the standard deviation is a function of the value of the mean. --- *(Note: The table above requires values for the mean and sample standard deviations to be filled in by the students during the exercise.)* In this exercise, students will take the given samples and calculate the mean and standard deviation to understand the relationship between these statistical measures. --- This page is intended to help students grasp the concept of mean and standard deviation, demonstrating that the variability of data (standard deviation) does not necessarily depend on the central tendency (mean) of the data. Rather, it depends on how spread out the values are from the mean. For example, in this exercise: - Sample A consists of lower values compared to Sample B and Sample C. - Despite the differences in the value ranges, students may observe how the standard deviations compare when they are calculated. --- #### Instructions: 1. Calculate the mean for each sample by summing all the data points in the sample and dividing by the number of data points. 2. Calculate the sample standard deviation for each sample using the formula for sample standard deviation. Formula for sample standard deviation: \[ s = \sqrt{\frac{1}{N-1} \sum_{i=1}^{N} (x_i - \bar{x})^2} \] Where \( N \) is the number of observations, \( x_i \) is each individual observation, and \( \bar{x} \) is the sample mean. Complete the table and choose the correct option for part (b) based on your understanding and calculations. --- **End of Exercise** ---
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![---
### Consider the following sample data:
- **Sample A:** 11, 22, 33
- **Sample B:** 81, 92, 103
- **Sample C:** 1,100; 1,111; 1,122
---
#### (a) Find the mean and standard deviation for each sample.
| | Sample A | Sample B | Sample C |
|------------------|--------------|--------------|--------------|
| **Mean** | | | |
| **Sample Standard Deviation** | | | |
#### (b) What does this exercise show about the standard deviation?
- The idea is to illustrate that the standard deviation is not a function of the value of the mean.
- The idea is to illustrate that the standard deviation is a function of the value of the mean.
---
*(Note: The table above requires values for the mean and sample standard deviations to be filled in by the students during the exercise.)*
In this exercise, students will take the given samples and calculate the mean and standard deviation to understand the relationship between these statistical measures.
---
This page is intended to help students grasp the concept of mean and standard deviation, demonstrating that the variability of data (standard deviation) does not necessarily depend on the central tendency (mean) of the data. Rather, it depends on how spread out the values are from the mean.
For example, in this exercise:
- Sample A consists of lower values compared to Sample B and Sample C.
- Despite the differences in the value ranges, students may observe how the standard deviations compare when they are calculated.
---
#### Instructions:
1. Calculate the mean for each sample by summing all the data points in the sample and dividing by the number of data points.
2. Calculate the sample standard deviation for each sample using the formula for sample standard deviation.
Formula for sample standard deviation:
\[ s = \sqrt{\frac{1}{N-1} \sum_{i=1}^{N} (x_i - \bar{x})^2} \]
Where \( N \) is the number of observations, \( x_i \) is each individual observation, and \( \bar{x} \) is the sample mean.
Complete the table and choose the correct option for part (b) based on your understanding and calculations.
---
**End of Exercise**
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4c7c255b-9578-426a-91b4-938323176667%2Fe05aea99-bc68-4bd5-85f9-d27ad7792283%2F35p6ufj.jpeg&w=3840&q=75)
Transcribed Image Text:---
### Consider the following sample data:
- **Sample A:** 11, 22, 33
- **Sample B:** 81, 92, 103
- **Sample C:** 1,100; 1,111; 1,122
---
#### (a) Find the mean and standard deviation for each sample.
| | Sample A | Sample B | Sample C |
|------------------|--------------|--------------|--------------|
| **Mean** | | | |
| **Sample Standard Deviation** | | | |
#### (b) What does this exercise show about the standard deviation?
- The idea is to illustrate that the standard deviation is not a function of the value of the mean.
- The idea is to illustrate that the standard deviation is a function of the value of the mean.
---
*(Note: The table above requires values for the mean and sample standard deviations to be filled in by the students during the exercise.)*
In this exercise, students will take the given samples and calculate the mean and standard deviation to understand the relationship between these statistical measures.
---
This page is intended to help students grasp the concept of mean and standard deviation, demonstrating that the variability of data (standard deviation) does not necessarily depend on the central tendency (mean) of the data. Rather, it depends on how spread out the values are from the mean.
For example, in this exercise:
- Sample A consists of lower values compared to Sample B and Sample C.
- Despite the differences in the value ranges, students may observe how the standard deviations compare when they are calculated.
---
#### Instructions:
1. Calculate the mean for each sample by summing all the data points in the sample and dividing by the number of data points.
2. Calculate the sample standard deviation for each sample using the formula for sample standard deviation.
Formula for sample standard deviation:
\[ s = \sqrt{\frac{1}{N-1} \sum_{i=1}^{N} (x_i - \bar{x})^2} \]
Where \( N \) is the number of observations, \( x_i \) is each individual observation, and \( \bar{x} \) is the sample mean.
Complete the table and choose the correct option for part (b) based on your understanding and calculations.
---
**End of Exercise**
---
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