To find the sample standard deviation of the numbers 2, 6, 15, 9, 11, 22, 1, 4, 8, 19, follow these steps:
1. **Calculate the Mean (Average):**
First, add all the numbers together and then divide by the count of numbers.
Sum = 2 + 6 + 15 + 9 + 11 + 22 + 1 + 4 + 8 + 19 = 97
Number of data points = 10
Mean = Sum / Number of data points = 97 / 10 = 9.7
2. **Calculate the Variance:**
For each number, subtract the mean and square the result. Then, find the average of these squared differences.
Squared differences:
(2 – 9.7)² = 59.29
(6 – 9.7)² = 13.69
(15 – 9.7)² = 28.09
(9 – 9.7)² = 0.49
(11 – 9.7)² = 1.69
(22 – 9.7)² = 151.29
(1 – 9.7)² = 75.69
(4 – 9.7)² = 32.49
(8 – 9.7)² = 2.89
(19 – 9.7)² = 86.49
Sum of squared differences = 59.29 + 13.69 + 28.09 + 0.49 + 1.69 + 151.29 + 75.69 + 32.49 + 2.89 + 86.49 = 452.10
Variance = Sum of squared differences / (Number of data points – 1) = 452.10 / 9 = 50.23
3. **Calculate the Standard Deviation:**
The standard deviation is the square root of the variance.
Standard Deviation = √50.23 ≈ 7.09
So, the sample standard deviation of the given numbers is approximately 7.09.