Question

The sum of mean and variance of a given set is 15/2 and their number of trials is 10, then find the value of variance?

Answer 1

Step 1: Define Mean and Variance
Let's denote the mean as μ and the variance as σ². We are given that their sum is 15/2.
μ + σ² = 15/2

Step 2: State the Number of Trials
We are also given that the number of trials is 10.
n = 10

Step 3: State the Relationship Between Variance and Mean
The problem provides a relationship between the variance and the mean: σ² = μ/n

Step 4: Substitute the Variance Relationship into the Sum Equation
Substitute σ² = μ/n into the equation μ + σ² = 15/2:
μ + (μ/n) = 15/2

Step 5: Multiply by n to Simplify
Multiply both sides of the equation by n:
nμ + μ = (15/2) * n

Step 6: Factor Out μ
Factor out μ:
μ * (n + 1) = (15/2) * n

Step 7: Solve for μ
Divide both sides of the equation by (n + 1):
μ = (15/2) * n / (n + 1)

Step 8: Substitute n = 10
Substitute the value of n = 10:
μ = (15/2) * 10 / (10 + 1)
μ = (15/2) * 10 / 11
μ = 150/22
μ = 75/11

Step 9: Calculate μ
μ = 75/11

Step 10: Substitute μ Back into the Variance Equation
Now we can substitute the value of μ back into the equation for the variance σ² = μ/n:
σ² = (75/11) / 10

Step 11: Calculate Variance
σ² = 75 / (11 * 10)
σ² = 75 / 110
σ² = 15 / 22

Step 12: State the Final Result
Therefore, the value of the variance is 15/22.