.What are the values of SS and variance s² for the following sample of n=3 scores? Sample: 1, 4, 7
.What are the values of SS and variance s² for the following sample of n=3 scores? Sample: 1, 4, 7
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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![**Question:** What are the values of SS and variance \( s^2 \) for the following sample of \( n = 3 \) scores?
**Sample:** 1, 4, 7
---
### Explanation:
To calculate the values of SS (Sum of Squares) and variance \( s^2 \) for the sample, follow these steps:
1. **Find the Mean:**
\[
\text{Mean} = \frac{1 + 4 + 7}{3} = \frac{12}{3} = 4
\]
2. **Calculate the Sum of Squares (SS):**
\[
SS = (1-4)^2 + (4-4)^2 + (7-4)^2 = (-3)^2 + 0^2 + 3^2 = 9 + 0 + 9 = 18
\]
3. **Compute the Variance \( s^2 \):**
- Since the sample size \( n = 3 \), use the formula for sample variance:
\[
s^2 = \frac{SS}{n-1} = \frac{18}{2} = 9
\]
Thus, for the given sample, Sum of Squares (SS) is 18, and the variance \( s^2 \) is 9.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F396cda7c-782c-4cc6-8ef0-da5ec17c422f%2Fde6c9673-bf8e-467b-8fc8-6221d0f66e36%2Flauv8s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:** What are the values of SS and variance \( s^2 \) for the following sample of \( n = 3 \) scores?
**Sample:** 1, 4, 7
---
### Explanation:
To calculate the values of SS (Sum of Squares) and variance \( s^2 \) for the sample, follow these steps:
1. **Find the Mean:**
\[
\text{Mean} = \frac{1 + 4 + 7}{3} = \frac{12}{3} = 4
\]
2. **Calculate the Sum of Squares (SS):**
\[
SS = (1-4)^2 + (4-4)^2 + (7-4)^2 = (-3)^2 + 0^2 + 3^2 = 9 + 0 + 9 = 18
\]
3. **Compute the Variance \( s^2 \):**
- Since the sample size \( n = 3 \), use the formula for sample variance:
\[
s^2 = \frac{SS}{n-1} = \frac{18}{2} = 9
\]
Thus, for the given sample, Sum of Squares (SS) is 18, and the variance \( s^2 \) is 9.
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