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.

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

a

step-by-step explanation: