Question 1180573: If you are rolling a fair die five times then sample size n=3. what is the population mean, population variance,and a population standard deviation? And What is the sample means,sample variances,& standard deviations?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's the breakdown of population and sample statistics for rolling a fair die:
**1. Population Statistics:**
When rolling a fair six-sided die, the possible outcomes are {1, 2, 3, 4, 5, 6}.
* **Population Mean (μ):**
μ = (1 + 2 + 3 + 4 + 5 + 6) / 6 = 21 / 6 = 3.5
* **Population Variance (σ²):**
First, calculate the squared deviations from the mean:
(1-3.5)² = 6.25
(2-3.5)² = 2.25
(3-3.5)² = 0.25
(4-3.5)² = 0.25
(5-3.5)² = 2.25
(6-3.5)² = 6.25
σ² = (6.25 + 2.25 + 0.25 + 0.25 + 2.25 + 6.25) / 6 = 17.5 / 6 ≈ 2.917
* **Population Standard Deviation (σ):**
σ = √σ² = √2.917 ≈ 1.708
**2. Sample Statistics:**
You've stated that the sample size *n* = 3. However, you haven't given me the actual outcomes of the three dice rolls. I need those three numbers to calculate the sample mean, variance, and standard deviation.
*Example:* Let's say you rolled a 2, a 4, and a 6.
* **Sample Mean (x̄):**
x̄ = (2 + 4 + 6) / 3 = 12 / 3 = 4
* **Sample Variance (s²):**
First, calculate the squared deviations from the sample mean:
(2-4)² = 4
(4-4)² = 0
(6-4)² = 4
s² = (4 + 0 + 4) / (3 - 1) = 8 / 2 = 4 (Note: We divide by *n*-1, not *n*, for sample variance)
* **Sample Standard Deviation (s):**
s = √s² = √4 = 2
**Provide me with the three numbers you rolled, and I'll calculate the actual sample mean, variance, and standard deviation for your specific sample.**
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