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Basic Computation: Variance, Standard Deviation Given the sample data 15 30 25 23 (a) Find the range. (b) Verify that Ex = 110 and Ex² = 2568. (c) Use the results of part (b) and appropriate computation formulas to com- pute the sample variance s² and sample standard deviation s. X: 17

Basic Computation: Variance, Standard Deviation Given the sample data 15 30 25 23 (a) Find the range. (b) Verify that Ex = 110 and Ex² = 2568. (c) Use the results of part (b) and appropriate computation formulas to com- pute the sample variance s² and sample standard deviation s. X: 17

MATLAB: An Introduction with Applications
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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Please answer number 13. Make sure to show work!! Thx!
### 12. Critical Thinking: Outliers One indicator of an outlier is that an observation is more than 2.5 standard deviations from the mean. Consider the data value 80. (a) If a data set has mean 70 and standard deviation 5, is 80 a suspect outlier? (b) If a data set has mean 70 and standard deviation 3, is 80 a suspect outlier? ### 13. Basic Computation: Variance, Standard Deviation Given the sample data: \[ x: 23 \quad 17 \quad 15 \quad 30 \quad 25 \] (a) Find the range. (b) Verify that \(\sum x = 110\) and \(\sum x^2 = 2568\). (c) Use the results of part (b) and appropriate computation formulas to compute the sample variance \(s^2\) and sample standard deviation \(s\). (d) Use the defining formulas to compute the sample variance \(s^2\) and sample standard deviation \(s\). (e) Suppose the given data comprise the entire population of all \(x\) values. Compute the population variance \(\sigma^2\) and population standard deviation \(\sigma\). ### Explanation **Problem 12:** This problem involves understanding outliers. An outlier is generally defined as a data point that is more than 2.5 standard deviations away from the mean. Based on the given scenarios, you would determine whether the value 80 is an outlier using the provided means and standard deviations. **Problem 13:** This problem involves basic computations of range, and variance and standard deviation for both sample and population data: 1. **Range:** The difference between the maximum and minimum values in the data set. 2. **Verification:** Confirm the sum of data points \(\sum x = 110\) and the sum of the squares of data points \(\sum x^2 = 2568\). 3. **Sample Variance and Standard Deviation:** Using formulas to compute these based on the sample data. 4. **Population Variance and Standard Deviation:** Assuming the sample data represents the entire population, compute these values.
Transcribed Image Text:### 12. Critical Thinking: Outliers One indicator of an outlier is that an observation is more than 2.5 standard deviations from the mean. Consider the data value 80. (a) If a data set has mean 70 and standard deviation 5, is 80 a suspect outlier? (b) If a data set has mean 70 and standard deviation 3, is 80 a suspect outlier? ### 13. Basic Computation: Variance, Standard Deviation Given the sample data: \[ x: 23 \quad 17 \quad 15 \quad 30 \quad 25 \] (a) Find the range. (b) Verify that \(\sum x = 110\) and \(\sum x^2 = 2568\). (c) Use the results of part (b) and appropriate computation formulas to compute the sample variance \(s^2\) and sample standard deviation \(s\). (d) Use the defining formulas to compute the sample variance \(s^2\) and sample standard deviation \(s\). (e) Suppose the given data comprise the entire population of all \(x\) values. Compute the population variance \(\sigma^2\) and population standard deviation \(\sigma\). ### Explanation **Problem 12:** This problem involves understanding outliers. An outlier is generally defined as a data point that is more than 2.5 standard deviations away from the mean. Based on the given scenarios, you would determine whether the value 80 is an outlier using the provided means and standard deviations. **Problem 13:** This problem involves basic computations of range, and variance and standard deviation for both sample and population data: 1. **Range:** The difference between the maximum and minimum values in the data set. 2. **Verification:** Confirm the sum of data points \(\sum x = 110\) and the sum of the squares of data points \(\sum x^2 = 2568\). 3. **Sample Variance and Standard Deviation:** Using formulas to compute these based on the sample data. 4. **Population Variance and Standard Deviation:** Assuming the sample data represents the entire population, compute these values.
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