SOLUTION: The following data give the yearly numbers of law enforcement officers killed in the United States over 10 years: 164, 165, 157, 164, 152, 147, 148, 131, 147, 155, calculate samp

Algebra ->  Probability-and-statistics -> SOLUTION: The following data give the yearly numbers of law enforcement officers killed in the United States over 10 years: 164, 165, 157, 164, 152, 147, 148, 131, 147, 155, calculate samp      Log On


   

Question 1190743: The following data give the yearly numbers of law enforcement officers killed in the United
States over 10 years: 164, 165, 157, 164, 152, 147, 148, 131, 147, 155, calculate sample
variance and standard deviation.
Answer by CPhill(1987) About Me  (Show Source):
You can put this solution on YOUR website!
Here's how to calculate the sample variance and standard deviation:
1. **Calculate the mean (average):**
Mean = (164 + 165 + 157 + 164 + 152 + 147 + 148 + 131 + 147 + 155) / 10 = 1530 / 10 = 153
2. **Calculate the squared differences from the mean:**
* (164 - 153)² = 121
* (165 - 153)² = 144
* (157 - 153)² = 16
* (164 - 153)² = 121
* (152 - 153)² = 1
* (147 - 153)² = 36
* (148 - 153)² = 25
* (131 - 153)² = 484
* (147 - 153)² = 36
* (155 - 153)² = 4
3. **Calculate the sum of squared differences:**
121 + 144 + 16 + 121 + 1 + 36 + 25 + 484 + 36 + 4 = 992
4. **Calculate the sample variance:**
Sample Variance = (Sum of Squared Differences) / (Number of Data Points - 1)
Sample Variance = 992 / (10 - 1) = 992 / 9 ≈ 110.22
5. **Calculate the sample standard deviation:**
Sample Standard Deviation = √(Sample Variance)
Sample Standard Deviation = √(110.22) ≈ 10.50
Therefore, the sample variance is approximately 110.22, and the sample standard deviation is approximately 10.50.