Write the formula for the sample mean, X, for ʼn data points. Write the formula for the sample variance, S², for n data points.
Write the formula for the sample mean, X, for ʼn data points. Write the formula for the sample variance, S², for n data points.
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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![**Understanding Sample Statistics**
**Sample Mean (\(\bar{X}\)):**
To calculate the sample mean for a set of \(n\) data points, use the formula:
\[
\bar{X} = \frac{1}{n} \sum_{i=1}^{n} X_i
\]
where \(\bar{X}\) is the sample mean, \(n\) is the number of data points, and \(X_i\) represents each individual data point.
**Sample Variance (\(S^2\)):**
The formula for the sample variance is as follows:
\[
S^2 = \frac{1}{n-1} \sum_{i=1}^{n} (X_i - \bar{X})^2
\]
In this formula, \(S^2\) is the sample variance, and \((X_i - \bar{X})^2\) is the squared deviation of each data point from the sample mean. The denominator \(n-1\) represents the degrees of freedom used in sample variance calculation. This adjustment is necessary to obtain an unbiased estimate of the population variance.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6e2f997-9120-4975-9388-a1bc7e4c3a16%2Fbdc4b48a-d9d2-49a5-8c8a-7ba7e38eeff1%2Fszhn8ad_processed.png&w=3840&q=75)
Transcribed Image Text:**Understanding Sample Statistics**
**Sample Mean (\(\bar{X}\)):**
To calculate the sample mean for a set of \(n\) data points, use the formula:
\[
\bar{X} = \frac{1}{n} \sum_{i=1}^{n} X_i
\]
where \(\bar{X}\) is the sample mean, \(n\) is the number of data points, and \(X_i\) represents each individual data point.
**Sample Variance (\(S^2\)):**
The formula for the sample variance is as follows:
\[
S^2 = \frac{1}{n-1} \sum_{i=1}^{n} (X_i - \bar{X})^2
\]
In this formula, \(S^2\) is the sample variance, and \((X_i - \bar{X})^2\) is the squared deviation of each data point from the sample mean. The denominator \(n-1\) represents the degrees of freedom used in sample variance calculation. This adjustment is necessary to obtain an unbiased estimate of the population variance.
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