Question

3. The following are the scores you shot in five rounds of golf: 70,80,75,75,80. The variance is: A. 3.74 C. 14 B. 196 D. 70​

Answer 1

Option C.

Explanation:

For a given set of N elements:

{x₁, x₂, ..., xₙ}

The mean is given by:

`M = (x_1 + x_2 + ... + x_n)/(N)`

And the variance is given by:

`v = ((x_1 - M)^2 + (x_2 - M)^2 + ... + (x_n - M)^2)/(N)`

Then for our set:

{70, 80 ,75, 75, 80}

We have 5 elements, then N = 5

The first thing we need to find is the mean.

`M = (70 + 80 + 75 + 75 + 80)/(5) = 76`

Then the variance will be:

`v = ((70 - 76)^2 + (80 - 76)^2 + (75 - 76)^2 + (75 - 76)^2 + (80 - 76)^2)/(5) = 14`

The correct option is C, 14.