Question

Question

Find the sample variance of the following set of data:
12, 7, 6, 4, 11.
Select the correct answer below:

Answer 1

To calculate the sample variance of the data set 12, 7, 6, 4, 11, we find the mean, subtract it from each data point, square the results, sum them up, and divide by one fewer than the number of data points. The sample variance is 11.5.

Step-by-step explanation:

To find the sample variance of the data set 12, 7, 6, 4, 11, we first calculate the mean (average) of these numbers. Then, we subtract the mean from each individual data point, square each of these results, sum up these squares, and finally divide by the number of data points minus one (n-1) because it's a sample variance, not a population variance.

1. Calculate the mean: (12 + 7 + 6 + 4 + 11) / 5 = 40 / 5 = 8.
2. Subtract the mean and square the differences: (12-8)², (7-8)², (6-8)², (4-8)², (11-8)² which are 16, 1, 4, 16, 9 respectively.
3. Sum up the squared differences: 16 + 1 + 4 + 16 + 9 = 46.
4. Divide by the number of data points minus one: 46 / (5-1) = 46 / 4 = 11.5.

Therefore, the sample variance of the data set is 11.5.

Answer 2

Variance is 256

Step-by-step explanation:

Variance:

`var = \frac{ ({ \sum x})^(2) }{n} - {( ( \sum x)/(n) })^(2)`

x is the number or item in the data

n is the number of terms

`{ \tt{ \sum x = (12 + 7 + 6 + 4 + 11)}} \\ { \tt{ \sum x = 40}}`

Therefore:

`variance = \frac{ {40}^(2) }{5} - { ((40)/(5)) }^(2) \\ \\ = 320 - 64 \\ variance = 256`