We determined the sum of the squared deviations to be Σ(x − x)2 = 21,912.1, and there are n = 10 observations. Substitute the values into the formula below and simplify to find the variance, s², and the sample standard deviation, s. (Round your answers to four decimals.) (x-x)² n-1 s² s²= 21,912.1 10 1 s² = 2434.6777 S = √√√√5² s=2434.6777 The sample standard deviation for the New Year's Day data is 2434.6777 X Recall that sample standard deviation is a measure of variation in the data set that describes how the data values spread away from the mean. Smaller standard deviation numbers indicate little variation in the data set while large standard deviation numbers indicate a lot of variation. X
We determined the sum of the squared deviations to be Σ(x − x)2 = 21,912.1, and there are n = 10 observations. Substitute the values into the formula below and simplify to find the variance, s², and the sample standard deviation, s. (Round your answers to four decimals.) (x-x)² n-1 s² s²= 21,912.1 10 1 s² = 2434.6777 S = √√√√5² s=2434.6777 The sample standard deviation for the New Year's Day data is 2434.6777 X Recall that sample standard deviation is a measure of variation in the data set that describes how the data values spread away from the mean. Smaller standard deviation numbers indicate little variation in the data set while large standard deviation numbers indicate a lot of variation. X
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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i don't understand how you find the standard deviation from the squared deviation?
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### Calculation of Variance and Sample Standard Deviation
We determined the sum of the squared deviations to be
\[ \sum (x - \bar{x})^2 = 21,912.1, \]
and there are \( n = 10 \) observations. Substitute the values into the formula below and simplify to find the variance, \( s^2 \), and the sample standard deviation, \( s \). (Round your answers to four decimals.)
\[ s^2 = \frac{\sum (x - \bar{x})^2}{n - 1} \]
\[ s^2 = \frac{21,912.1}{10 - 1} \]
\[ s^2 = 2434.6777 \]
\[ s = \sqrt{s^2} \]
\[ s = 2434.6777 \]
The sample standard deviation for the New Year's Day data is \( 2434.6777 \).
Recall that sample standard deviation is a measure of variation in the data set that describes how the data values spread away from the mean. Smaller standard deviation numbers indicate little variation in the data set while large standard deviation numbers indicate a lot of variation.
##### Explanation of Each Step:
1. **Sum of Squared Deviations**: The given sum of squared deviations from the mean which is \( 21,912.1 \).
2. **Number of Observations (\( n \))**: The total number of observations is 10.
3. **Variance (\( s^2 \)) Calculation**:
- The variance is obtained by dividing the sum of squared deviations by \( n-1 \).
- Substitution yields \( s^2 = \frac{21,912.1}{10 - 1} = 2434.6777 \).
4. **Sample Standard Deviation (\( s \)) Calculation**:
- The sample standard deviation is the square root of the variance.
- Therefore, \( s = \sqrt{2434.6777} \).
These calculations demonstrate how to find the sample variance and standard deviation, which are key indicators of data spread and variability.
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Transcribed Image Text:---
### Calculation of Variance and Sample Standard Deviation
We determined the sum of the squared deviations to be
\[ \sum (x - \bar{x})^2 = 21,912.1, \]
and there are \( n = 10 \) observations. Substitute the values into the formula below and simplify to find the variance, \( s^2 \), and the sample standard deviation, \( s \). (Round your answers to four decimals.)
\[ s^2 = \frac{\sum (x - \bar{x})^2}{n - 1} \]
\[ s^2 = \frac{21,912.1}{10 - 1} \]
\[ s^2 = 2434.6777 \]
\[ s = \sqrt{s^2} \]
\[ s = 2434.6777 \]
The sample standard deviation for the New Year's Day data is \( 2434.6777 \).
Recall that sample standard deviation is a measure of variation in the data set that describes how the data values spread away from the mean. Smaller standard deviation numbers indicate little variation in the data set while large standard deviation numbers indicate a lot of variation.
##### Explanation of Each Step:
1. **Sum of Squared Deviations**: The given sum of squared deviations from the mean which is \( 21,912.1 \).
2. **Number of Observations (\( n \))**: The total number of observations is 10.
3. **Variance (\( s^2 \)) Calculation**:
- The variance is obtained by dividing the sum of squared deviations by \( n-1 \).
- Substitution yields \( s^2 = \frac{21,912.1}{10 - 1} = 2434.6777 \).
4. **Sample Standard Deviation (\( s \)) Calculation**:
- The sample standard deviation is the square root of the variance.
- Therefore, \( s = \sqrt{2434.6777} \).
These calculations demonstrate how to find the sample variance and standard deviation, which are key indicators of data spread and variability.
---
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