### Population Data and Standard Deviation Calculation #### Given Data: A set of data for a population where \( N = 10 \) is as follows: \[ 7, 5, 11, 8, 3, 6, 2, 1, 9, 8 \] #### Task: **a) Calculate the population standard deviation.** To calculate the standard deviation, follow these steps: 1. **Find the Mean (\(\mu\)):** \[ \mu = \frac{\sum X_i}{N} = \frac{7 + 5 + 11 + 8 + 3 + 6 + 2 + 1 + 9 + 8}{10} \] 2. **Calculate the Deviations from the Mean:** For each data point \( X_i \), compute \( (X_i - \mu)^2 \). 3. **Find the Variance (\(\sigma^2\)):** \[ \sigma^2 = \frac{\sum (X_i - \mu)^2}{N} \] 4. **Calculate the Standard Deviation (\(\sigma\)):** \[ \sigma = \sqrt{\sigma^2} \] This process will yield the population standard deviation for the given data set.
### Population Data and Standard Deviation Calculation #### Given Data: A set of data for a population where \( N = 10 \) is as follows: \[ 7, 5, 11, 8, 3, 6, 2, 1, 9, 8 \] #### Task: **a) Calculate the population standard deviation.** To calculate the standard deviation, follow these steps: 1. **Find the Mean (\(\mu\)):** \[ \mu = \frac{\sum X_i}{N} = \frac{7 + 5 + 11 + 8 + 3 + 6 + 2 + 1 + 9 + 8}{10} \] 2. **Calculate the Deviations from the Mean:** For each data point \( X_i \), compute \( (X_i - \mu)^2 \). 3. **Find the Variance (\(\sigma^2\)):** \[ \sigma^2 = \frac{\sum (X_i - \mu)^2}{N} \] 4. **Calculate the Standard Deviation (\(\sigma\)):** \[ \sigma = \sqrt{\sigma^2} \] This process will yield the population standard deviation for the given data set.
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
![### Population Data and Standard Deviation Calculation
#### Given Data:
A set of data for a population where \( N = 10 \) is as follows:
\[ 7, 5, 11, 8, 3, 6, 2, 1, 9, 8 \]
#### Task:
**a) Calculate the population standard deviation.**
To calculate the standard deviation, follow these steps:
1. **Find the Mean (\(\mu\)):**
\[
\mu = \frac{\sum X_i}{N} = \frac{7 + 5 + 11 + 8 + 3 + 6 + 2 + 1 + 9 + 8}{10}
\]
2. **Calculate the Deviations from the Mean:**
For each data point \( X_i \), compute \( (X_i - \mu)^2 \).
3. **Find the Variance (\(\sigma^2\)):**
\[
\sigma^2 = \frac{\sum (X_i - \mu)^2}{N}
\]
4. **Calculate the Standard Deviation (\(\sigma\)):**
\[
\sigma = \sqrt{\sigma^2}
\]
This process will yield the population standard deviation for the given data set.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc37dbff0-e053-476c-a940-a199db5d9106%2F12fe3224-c1c4-43d5-ab66-918126a0b45d%2F9ndkx2e.jpeg&w=3840&q=75)
Transcribed Image Text:### Population Data and Standard Deviation Calculation
#### Given Data:
A set of data for a population where \( N = 10 \) is as follows:
\[ 7, 5, 11, 8, 3, 6, 2, 1, 9, 8 \]
#### Task:
**a) Calculate the population standard deviation.**
To calculate the standard deviation, follow these steps:
1. **Find the Mean (\(\mu\)):**
\[
\mu = \frac{\sum X_i}{N} = \frac{7 + 5 + 11 + 8 + 3 + 6 + 2 + 1 + 9 + 8}{10}
\]
2. **Calculate the Deviations from the Mean:**
For each data point \( X_i \), compute \( (X_i - \mu)^2 \).
3. **Find the Variance (\(\sigma^2\)):**
\[
\sigma^2 = \frac{\sum (X_i - \mu)^2}{N}
\]
4. **Calculate the Standard Deviation (\(\sigma\)):**
\[
\sigma = \sqrt{\sigma^2}
\]
This process will yield the population standard deviation for the given data set.
Expert Solution
Step 1
We have given that The data are 7,5,11,8,3,6,2,1,9,8
Find the standard deviation
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman