Question

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Answer 1

Answer:

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

$Mean=\frac{\sum x}{n}$

$Mean=\frac{4+16+21+32+11+12}{6}=\frac{96}{6}=16$

The value of variance for the data set is

$\sigma^2=\frac{\sum (x-\overline{x})^2}{n}$

$\sigma^2=\frac{(4-16)^2+(16-16)^2+(21-16)^2+(32-16)^2+(11-16)^2+(12-16)^2}{6}$

$\sigma^2=\frac{466}{6}$

$\sigma^2\approx 77.67$

Therefore the variance for the data set is 77.67.

Answer 2

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

$\mu = 96/6 = 16$

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

$s = (4 - 16)^2 + (16 - 16)^2 + (21 - 16)^2 + (32 - 16)^2 + (11 - 16)^2 + (12 - 16)^2$

$s= 466$

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:

$\sigma^2 = 466/5 = 93.2$

Answer: 93.2