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The following data values represent a sample. What is the variance of the sample? x = 9. Use the information in the table to help you. 13 9. 11 7. (x,- x)² 16 4 16 LO

The following data values represent a sample. What is the variance of the sample? x = 9. Use the information in the table to help you. 13 9. 11 7. (x,- x)² 16 4 16 LO

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Certainly! Here's a transcription suitable for an educational website: --- **Multiple Choice Options:** - **A.** 10 - **B.** 3.8 - **C.** 4.5 - **D.** 8 --- *Note: The image contains a multiple-choice list of options labeled A, B, C, and D, each followed by a numerical value. There are no graphs or diagrams present in this image.*
Transcribed Image Text:Certainly! Here's a transcription suitable for an educational website: --- **Multiple Choice Options:** - **A.** 10 - **B.** 3.8 - **C.** 4.5 - **D.** 8 --- *Note: The image contains a multiple-choice list of options labeled A, B, C, and D, each followed by a numerical value. There are no graphs or diagrams present in this image.*
**Understanding Sample Variance** The following data values represent a sample. We aim to determine the variance of this sample using the given information. **Given**: - Sample mean (\(\bar{x}\)) = 9 **Data Values and Deviations**: | \(x\) | 13 | 9 | 11 | 7 | 5 | |------------|----|---|----|---|---| | \((x_i - \bar{x})^2\) | 16 | 0 | 4 | 4 | 16 | **Explanation**: - The top row (\(x\)) lists the individual data points of the sample: 13, 9, 11, 7, and 5. - The bottom row \((x_i - \bar{x})^2\) represents the squared deviations of each data point from the mean (9). To find the variance, follow these steps: 1. Calculate the squared deviation for each data point as shown in the table. 2. Sum all the squared deviations: \(16 + 0 + 4 + 4 + 16\). 3. Divide the sum by the number of data points minus one (n-1, where n is the sample size) to get the sample variance. This method helps understand how data points in a sample vary with respect to the mean.
Transcribed Image Text:**Understanding Sample Variance** The following data values represent a sample. We aim to determine the variance of this sample using the given information. **Given**: - Sample mean (\(\bar{x}\)) = 9 **Data Values and Deviations**: | \(x\) | 13 | 9 | 11 | 7 | 5 | |------------|----|---|----|---|---| | \((x_i - \bar{x})^2\) | 16 | 0 | 4 | 4 | 16 | **Explanation**: - The top row (\(x\)) lists the individual data points of the sample: 13, 9, 11, 7, and 5. - The bottom row \((x_i - \bar{x})^2\) represents the squared deviations of each data point from the mean (9). To find the variance, follow these steps: 1. Calculate the squared deviation for each data point as shown in the table. 2. Sum all the squared deviations: \(16 + 0 + 4 + 4 + 16\). 3. Divide the sum by the number of data points minus one (n-1, where n is the sample size) to get the sample variance. This method helps understand how data points in a sample vary with respect to the mean.
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