→ Standard Dev 2 S=√ Σ(4-6.2) ² 3-1
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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Question
![**Topic: Standard Deviation Calculation**
---
To calculate the Standard Deviation (S) of a given dataset, follow the below formula:
\[ S = \sqrt{ \frac{ \sum (x_i - \bar{x})^2 }{N-1} } \]
Where:
- \( \sum \) denotes the summation.
- \( x_i \) represents each data point in the dataset.
- \( \bar{x} \) is the mean (average) value of the dataset.
- \( N \) is the number of data points in the dataset.
In the example given:
\[ S = \sqrt{ \frac{ \sum (4 - 6.27)^2 }{3-1} } \]
Let's break this down step-by-step:
1. **Determine the mean (\( \bar{x} \))**:
- According to the formula, \( \bar{x} \) is given as 6.27.
2. **Calculate the variance ( \(s^2\) )**:
- Subtract the mean from each data point and then square the result.
- Sum these squared values.
- Divide by \( N - 1 \) (Bessel's correction for an unbiased estimate of population variance).
In the given formula: \( \sum (4 - 6.27)^2 \)
3. **Simplify the calculation**:
- Calculate \( (4 - 6.27)^2 \)
- Then, sum up the results.
- Divide the sum by \( N - 1 \) (in this case, `3-1`).
4. **Take the square root of the variance to obtain the Standard Deviation**.
Following these steps, you can calculate the standard deviation for any dataset.
---
This explanation covers the detailed process and formula used for calculating standard deviation as shown in the provided image.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F896b330c-0f31-4d4e-9300-b71637ec8079%2Ffe4c9768-fdb9-4a5d-bf7e-fa61d80f11e4%2Fv47h95b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Topic: Standard Deviation Calculation**
---
To calculate the Standard Deviation (S) of a given dataset, follow the below formula:
\[ S = \sqrt{ \frac{ \sum (x_i - \bar{x})^2 }{N-1} } \]
Where:
- \( \sum \) denotes the summation.
- \( x_i \) represents each data point in the dataset.
- \( \bar{x} \) is the mean (average) value of the dataset.
- \( N \) is the number of data points in the dataset.
In the example given:
\[ S = \sqrt{ \frac{ \sum (4 - 6.27)^2 }{3-1} } \]
Let's break this down step-by-step:
1. **Determine the mean (\( \bar{x} \))**:
- According to the formula, \( \bar{x} \) is given as 6.27.
2. **Calculate the variance ( \(s^2\) )**:
- Subtract the mean from each data point and then square the result.
- Sum these squared values.
- Divide by \( N - 1 \) (Bessel's correction for an unbiased estimate of population variance).
In the given formula: \( \sum (4 - 6.27)^2 \)
3. **Simplify the calculation**:
- Calculate \( (4 - 6.27)^2 \)
- Then, sum up the results.
- Divide the sum by \( N - 1 \) (in this case, `3-1`).
4. **Take the square root of the variance to obtain the Standard Deviation**.
Following these steps, you can calculate the standard deviation for any dataset.
---
This explanation covers the detailed process and formula used for calculating standard deviation as shown in the provided image.
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