**Calculating Mean and Standard Deviation** We are going to calculate the mean and standard deviation for the following set of sample data by hand. Round all values to 4 decimal places where possible. Sample Data: \(10, \ 4, \ 8, \ 5, \ 3\) **Steps:** a) **Calculate the Mean** Add all the numbers together and divide by 5 (the number of data points). \[ \bar{x} = \] b) **Fill in the Table** | \(x\) | \(x - \bar{x}\) | \((x - \bar{x})^2\) | |------|----------------|---------------------| | 10 | | | | 4 | | | | 8 | | | | 5 | | | | 3 | | | | **Total** | | | c) **Calculate the Standard Deviation** The formula for standard deviation is: \[ s = \sqrt{\frac{\sum (x - \bar{x})^2}{n - 1}} \] where \(\sum\) means sum, and \(n\) is the number of data points. \[ s = \] **Instructions:** 1. Compute the mean by adding all the sample data and dividing by 5. 2. Use the mean to fill in the table, calculating each deviation \((x - \bar{x})\) and its square \((x - \bar{x})^2\). 3. Sum the squared deviations, then use the standard deviation formula to find \(s\).
**Calculating Mean and Standard Deviation** We are going to calculate the mean and standard deviation for the following set of sample data by hand. Round all values to 4 decimal places where possible. Sample Data: \(10, \ 4, \ 8, \ 5, \ 3\) **Steps:** a) **Calculate the Mean** Add all the numbers together and divide by 5 (the number of data points). \[ \bar{x} = \] b) **Fill in the Table** | \(x\) | \(x - \bar{x}\) | \((x - \bar{x})^2\) | |------|----------------|---------------------| | 10 | | | | 4 | | | | 8 | | | | 5 | | | | 3 | | | | **Total** | | | c) **Calculate the Standard Deviation** The formula for standard deviation is: \[ s = \sqrt{\frac{\sum (x - \bar{x})^2}{n - 1}} \] where \(\sum\) means sum, and \(n\) is the number of data points. \[ s = \] **Instructions:** 1. Compute the mean by adding all the sample data and dividing by 5. 2. Use the mean to fill in the table, calculating each deviation \((x - \bar{x})\) and its square \((x - \bar{x})^2\). 3. Sum the squared deviations, then use the standard deviation formula to find \(s\).
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
![**Calculating Mean and Standard Deviation**
We are going to calculate the mean and standard deviation for the following set of sample data by hand. Round all values to 4 decimal places where possible.
Sample Data: \(10, \ 4, \ 8, \ 5, \ 3\)
**Steps:**
a) **Calculate the Mean**
Add all the numbers together and divide by 5 (the number of data points).
\[
\bar{x} =
\]
b) **Fill in the Table**
| \(x\) | \(x - \bar{x}\) | \((x - \bar{x})^2\) |
|------|----------------|---------------------|
| 10 | | |
| 4 | | |
| 8 | | |
| 5 | | |
| 3 | | |
| **Total** | | |
c) **Calculate the Standard Deviation**
The formula for standard deviation is:
\[
s = \sqrt{\frac{\sum (x - \bar{x})^2}{n - 1}}
\]
where \(\sum\) means sum, and \(n\) is the number of data points.
\[
s =
\]
**Instructions:**
1. Compute the mean by adding all the sample data and dividing by 5.
2. Use the mean to fill in the table, calculating each deviation \((x - \bar{x})\) and its square \((x - \bar{x})^2\).
3. Sum the squared deviations, then use the standard deviation formula to find \(s\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffbac2364-844d-4c30-bd9e-8f0fe127443d%2F9cd5e8b0-94a0-4f20-bee2-3c791894f176%2Fddvysxi_processed.png&w=3840&q=75)
Transcribed Image Text:**Calculating Mean and Standard Deviation**
We are going to calculate the mean and standard deviation for the following set of sample data by hand. Round all values to 4 decimal places where possible.
Sample Data: \(10, \ 4, \ 8, \ 5, \ 3\)
**Steps:**
a) **Calculate the Mean**
Add all the numbers together and divide by 5 (the number of data points).
\[
\bar{x} =
\]
b) **Fill in the Table**
| \(x\) | \(x - \bar{x}\) | \((x - \bar{x})^2\) |
|------|----------------|---------------------|
| 10 | | |
| 4 | | |
| 8 | | |
| 5 | | |
| 3 | | |
| **Total** | | |
c) **Calculate the Standard Deviation**
The formula for standard deviation is:
\[
s = \sqrt{\frac{\sum (x - \bar{x})^2}{n - 1}}
\]
where \(\sum\) means sum, and \(n\) is the number of data points.
\[
s =
\]
**Instructions:**
1. Compute the mean by adding all the sample data and dividing by 5.
2. Use the mean to fill in the table, calculating each deviation \((x - \bar{x})\) and its square \((x - \bar{x})^2\).
3. Sum the squared deviations, then use the standard deviation formula to find \(s\).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
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