Question

Ompute the (sample) variance and standard deviation of the data sample. (Round your answers to two decimal places.) −6, 7, 7, 7, 15

variance ______
standard deviation _____

Answer 1

The sample variance is 54 and the sample standard deviation is approximately 7.35.

Step-by-step explanation:

The sample variance is calculated as the average of the squared differences between each data point and the sample mean:

1. Find the sample mean: (-6 + 7 + 7 + 7 + 15) / 5 = 6

2. Calculate the squared differences: (-6-6)^2 + (7-6)^2 + (7-6)^2 + (7-6)^2 + (15-6)^2 = 216

3. Calculate the sample variance: 216 / (5-1) = 54

4. Calculate the sample standard deviation: √54 ≈ 7.35

Answer 2

The sample variance for the data (-6, 7, 7, 7, 15) is calculated to be 57, and the sample standard deviation, rounded to two decimal places, is 7.55.

Step-by-step explanation:

To compute the sample variance and standard deviation of the data sample (-6, 7, 7, 7, 15), we follow these steps:

1. 
   
3. Calculate the mean of the sample.
4. 
   
6. Subtract the mean from each data point and square the result.
7. 
   
9. Sum those squared differences.
10. 
    
12. Divide the sum by the sample size minus one to get the sample variance.
13. 
    
15. Take the square root of the variance to get the sample standard deviation.

Let's do the calculations:

1. Mean (μ) = (-6+7+7+7+15) / 5 = 30 / 5 = 6

2. The squared differences are: (-6-6)², (7-6)², (7-6)², (7-6)², (15-6)² = 144, 1, 1, 1, 81.

3. Sum = 144 + 1 + 1 + 1 + 81 = 228

4. Sample variance (s²) = 228 / (5-1) = 228 / 4 = 57

5. Sample standard deviation (s) = √57 = 7.55 (rounded to two decimal places)

Therefore, the sample variance is 57, and the standard deviation is 7.55.