Calculate the variance and standard error for the following bird weight data from a publication by Baldwin & Kendeigh written in 1938. The next 5 numbers are the data. The units are grams. 11.4, 11.9, 12.4, 12.9, 14.1 n × (E[x²] - [E(x)²]) n - 1 co =
Calculate the variance and standard error for the following bird weight data from a publication by Baldwin & Kendeigh written in 1938. The next 5 numbers are the data. The units are grams. 11.4, 11.9, 12.4, 12.9, 14.1 n × (E[x²] - [E(x)²]) n - 1 co =
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 Variance and Standard Error for Bird Weight Data
#### Bird Weight Data
The data provided for the bird weights is obtained from a publication by Baldwin & Kendeigh written in 1938. The weights are given in grams:
- 11.4 grams
- 11.9 grams
- 12.4 grams
- 12.9 grams
- 14.1 grams
#### Variance and Standard Error Calculation
To calculate the variance (\(s^2\)) for the given data, we can use the following formula:
\[
s^2 = \frac{n}{n - 1} \times (\mathbb{E}[x^2] - [\mathbb{E}(x)]^2)
\]
where:
- \( n \) is the number of data points,
- \(\mathbb{E}[x^2]\) is the expected value of the square of the data points,
- \(\mathbb{E}(x)\) is the expected value of the data points.
The above formula helps in estimating the variance by using the sample data in such a way that it corrects for biases.
##### Detailed Explanation:
1. **Expected Value of \(x\)** (\(\mathbb{E}(x)\)): It's the mean of the sample data.
2. **Expected Value of \(x^2\)** (\(\mathbb{E}[x^2]\)): This is calculated by taking the mean of each data point squared.
Next, we adjust our variance by multiplying by \(\frac{n}{n-1}\) to deal with bias in the sample variance estimate.
By calculating the variance first, we can then infer the standard error if needed by taking the square root of the variance divided by the number of samples.
No graphical representation is provided in the original document; the formulation is purely numerical and mathematical.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feceb8058-c7a9-4ec1-9952-bafa6949c626%2Fbdb391c4-1180-4cee-8468-fa1c2719adf1%2Fo008gfz_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculating Variance and Standard Error for Bird Weight Data
#### Bird Weight Data
The data provided for the bird weights is obtained from a publication by Baldwin & Kendeigh written in 1938. The weights are given in grams:
- 11.4 grams
- 11.9 grams
- 12.4 grams
- 12.9 grams
- 14.1 grams
#### Variance and Standard Error Calculation
To calculate the variance (\(s^2\)) for the given data, we can use the following formula:
\[
s^2 = \frac{n}{n - 1} \times (\mathbb{E}[x^2] - [\mathbb{E}(x)]^2)
\]
where:
- \( n \) is the number of data points,
- \(\mathbb{E}[x^2]\) is the expected value of the square of the data points,
- \(\mathbb{E}(x)\) is the expected value of the data points.
The above formula helps in estimating the variance by using the sample data in such a way that it corrects for biases.
##### Detailed Explanation:
1. **Expected Value of \(x\)** (\(\mathbb{E}(x)\)): It's the mean of the sample data.
2. **Expected Value of \(x^2\)** (\(\mathbb{E}[x^2]\)): This is calculated by taking the mean of each data point squared.
Next, we adjust our variance by multiplying by \(\frac{n}{n-1}\) to deal with bias in the sample variance estimate.
By calculating the variance first, we can then infer the standard error if needed by taking the square root of the variance divided by the number of samples.
No graphical representation is provided in the original document; the formulation is purely numerical and mathematical.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 2 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