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

1. Simplify the Integrand:
We are given the equation: \[ \mu + \sigma^2 = \frac{15}{2} \] where \( \mu \) is the mean and \( \sigma^2 \) is the variance.

2. Apply the Relationship Between Variance and Mean:
The relationship \( \sigma^2 = \frac{\mu}{n} \) is given. Substituting this into the sum equation: \[ \mu + \frac{\mu}{n} = \frac{15}{2} \]

3. Solve for \( \mu \):
Multiply through by \( n \), factor out \( \mu \), and solve: \[ \mu = \frac{\frac{15}{2} \cdot n}{n + 1} \] Substituting \( n = 10 \): \[ \mu = \frac{75}{11} \]

4. Calculate \( \sigma^2 \):
Substitute \( \mu = \frac{75}{11} \) into \( \sigma^2 = \frac{\mu}{n} \): \[ \sigma^2 = \frac{75}{110} = \frac{15}{22} \]

Final Answer:
Therefore, the variance is: \[ \sigma^2 = \frac{15}{22} \]