The mean is 6, the variance is 4, and the standard deviation is 2.
How the mean, variance, and standard deviation are computed:
The mean (expected value) of a random variable is the sum of the product of each outcome and its probability.
Mean (μ): μ = Σ [x * P(x)] = 1*(1/21) + 2*(1/21) + 3*(1/21) + 4*(1/21) + 5*(1/21) + 6*(1/21) + 7*(5/7) = 6
The variance is the sum of the squared difference between each outcome and the mean, multiplied by the probability of the outcome.
Variance (σ²): σ² = Σ [(x - μ)² * P(x)] = (1-6)²*(1/21) + (2-6)²*(1/21) + (3-6)²*(1/21) + (4-6)²*(1/21) + (5-6)²*(1/21) + (6-6)²*(1/21) + (7-6)²*(5/7) = 4
The standard deviation is the square root of the variance.
Standard Deviation (σ): σ = √σ² = √4 = 2
Thus, the mean is 6, the variance is 4, and the standard deviation is 2.
Complete Question:
A spinner has the following outcomes and probabilities:
Outcome (x) Probabily P(x)
1 1/21
2 1/21
3 1/21
4 1/21
5 1/21
6 1/21
7 5/7
Compute the mean, variance, and standard deviation.