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

Answer:

Option C.

Step-by-step explanation:

For a given set of N elements:

{x₁, x₂, ..., xₙ}

The mean is given by:

$M = \frac{x_1 + x_2 + ... + x_n}{N}$

And the variance is given by:

$v = \frac{(x_1 - M)^2 + (x_2 - M)^2 + ... + (x_n - M)^2}{N}$

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.

$M = \frac{70 + 80 + 75 + 75 + 80}{5} = 76$

Then the variance will be:

$v = \frac{(70 - 76)^2 + (80 - 76)^2 + (75 - 76)^2 + (75 - 76)^2 + (80 - 76)^2}{5} = 14$

The correct option is C, 14.