Question

The formula for the standard deviation of a sample is: s=√1/n−1​∑ᵢ₌₁ⁿ​(xi​−xˉ)²​. Select the true statement for the following data set that has a mean of 8: 4,6,6,6,9,9,12,12. Answer choices are rounded to the hundredths place. The variance is 8.86 and the standard deviation is 2.98.

a. The variance is 8.86 and the standard deviation is 2.98.
b. The variance is 2.98 and the standard deviation is 8.86.
c. The variance is 8.86 and the standard deviation is 7.50.
d. The variance is 7.50 and the standard deviation is 2.98.

Answer 1

The data set given has a mean of 8. Using the formula for the standard deviation of a sample, the variance is 8.86 and the standard deviation is 2.98.

So, the answer is c. The variance is 8.86, and the standard deviation is 2.98.

Step-by-step explanation:

The formula for the standard deviation of a sample is: s = √(1/n−1)∑ᵢ₌₁ⁿ(xi−xˉ)². In this case, the data set given has a mean of 8 and is as follows: 4, 6, 6, 6, 9, 9, 12, 12. To find the variance, we first need to calculate the deviations from the mean for each data point. Then, we square each deviation and sum them up.

The data set given has a mean of 8. Using the formula for the standard deviation of a sample, the variance is 8.86 and the standard deviation is 2.98.

Finally, we divide this sum by n-1, where n is the sample size. The square root of the variance gives us the standard deviation. Using this process, the variance is 8.86 and the standard deviation is 2.98. Therefore, the correct answer is a. The variance is 8.86 and the standard deviation is 2.98.