Brainliest + points calculate the variance for the data set. show all of your steps. { 4 , 16 , 21 , 32 , 11 , 12

There are a few different ways to calculate the variance.  Let's calculate the mean first, then the sum of the squared deviations from the mean and then we'll talk again.

{ 4 ,  16 ,  21 ,  32 ,  11 ,  12 }

Those add to 96 and there are 6 of them so a mean of

Now let's add up the squared deviations from the mean,

Since we used one of our six degrees of freedom to calculate the mean we have five left so we divide by five for the unbiased sample variance:

93.2

The variance for the data set is 77.67.

Step-by-step explanation:

The given data set is

{4, 16, 21, 32, 11, 12}

Mean of the data set is

The value of variance for the data set is

Therefore the variance for the data set is 77.67.

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.