Question

Find the sample vamance and the standard deviation for the following sample. Round the answers to at least two decimal places as needed.

17 30 23 15 12
The sample variance is ____
The simple standard devistion is _____

Answer 1

The sample variance for the given numbers is 57.55, and the standard deviation is 7.59 when rounded to two decimal places.

Step-by-step explanation:

To calculate the sample variance and the standard deviation for the given set of numbers (17, 30, 23, 15, 12), we will follow these steps:

1. Find the mean of the sample by summing up the numbers and dividing by the number of observations.
2. Subtract the mean from each number to find the deviations.
3. Square the deviations.
4. Add up the squared deviations.
5. Divide this sum by one less than the number of observations to find the sample variance.
6. Take the square root of the variance to find the standard deviation.

Now let's calculate:

1. The mean = (17 + 30 + 23 + 15 + 12) / 5 = 97 / 5 = 19.4
2. Squared deviations = (17-19.4)^2 + (30-19.4)^2 + (23-19.4)^2 + (15-19.4)^2 + (12-19.4)^2 = 230.2
3. The sample variance = 230.2 / (5-1) = 230.2 / 4 = 57.55
4. The standard deviation = √57.55 = 7.59 (to two decimal places)