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

Let's denote the mean as μ and the variance as σ².

We know that the sum of the mean and variance is 15/2:

μ + σ² = 15/2

We also know that the number of trials is 10:

n = 10

The relationship between the variance and the number of trials is given by:

σ² = μ/n

Substituting this relationship into the equation for the sum:

μ + (μ/n) = 15/2

Multiplying both sides of the equation by n:

nμ + μ = (15/2) * n

Factoring out μ:

μ * (n + 1) = (15/2) * n

Dividing both sides of the equation by (n + 1):

μ = (15/2) * n / (n + 1)

Substituting the value of n:

μ = (15/2) * 10 / (10 + 1) μ = 15/2

Now we can substitute the value of μ back into the equation for the variance:

σ² = μ/n σ² = (15/2) / 10 σ² = 3/4

Therefore, the value of the variance is 3/4.