Final answer:
To calculate the standard deviation (s) for the given data set, we find the mean, subtract it from each data point and square the results, calculate the mean of these squares, and take the square root. The calculated standard deviation is 4.55, which does not match any of the provided options.
Step-by-step explanation:
Calculating the Standard Deviation of a Data Set
To compute the standard deviation (s) for the data set 9, 6, 8, 14, 17, follow these steps:
- Find the mean of the data set.
- Subtract the mean from each data point and square the result.
- Calculate the average of these squared differences.
- Take the square root of the average to get the standard deviation.
First, calculate the mean (average): (9 + 6 + 8 + 14 + 17) / 5 = 54 / 5 = 10.8.
Next, subtract the mean from each data point, square the differences, and find the sum:
(9 - 10.8)² + (6 - 10.8)² + (8 - 10.8)² + (14 - 10.8)² + (17 - 10.8)²
= (1.8)² + (-4.8)² + (-2.8)² + (3.2)² + (6.2)²
= 3.24 + 23.04 + 7.84 + 10.24 + 38.44 = 82.8.
Divide this sum by the number of data points minus one (n-1) for the sample variance: 82.8 / (5 - 1) = 82.8 / 4 = 20.7.
Finally, take the square root of the variance to find the standard deviation: √20.7 = 4.55
Comparing the calculated standard deviation to the options provided (3.32, 4.18, 4.74, 5.82), none of them matches the calculated value 4.55.