Final answer:
The standard deviation for the given sample data is calculated step-by-step, resulting in an approximate value of 13.11, which suggests that the closest answer choice is C) 13.78.
Step-by-step explanation:
The question asks to find the standard deviation for the sample data: 20.0, 21.5, 27.4, 47.3, 13.1, 11.1. To calculate the sample standard deviation, we will use the following steps:
- Calculate the sample mean (average).
- Find the square of the difference between each data point and the sample mean.
- Sum up these squared differences.
- Divide the sum by the sample size minus one to find the variance.
- Take the square root of the variance to find the sample standard deviation.
Performing these calculations step-by-step:
- The sample mean = (20.0 + 21.5 + 27.4 + 47.3 + 13.1 + 11.1) / 6 = 140.4 / 6 = 23.4.
- Squared differences = (20.0 - 23.4)^2 + (21.5 - 23.4)^2 + (27.4 - 23.4)^2 + (47.3 - 23.4)^2 + (13.1 - 23.4)^2 + (11.1 - 23.4)^2.
- Sum of squared differences = 11.56 + 3.61 + 16.00 + 571.21 + 106.09 + 151.29 = 859.76.
- Variance = 859.76 / (6 - 1) = 859.76 / 5 = 171.952.
- Sample standard deviation = √171.952 = 13.1144, which when rounded to two decimal places is 13.11.
Therefore, the closest answer from the given options is C) 13.78, although the exact calculation gives a sample standard deviation closer to 13.11 which is not listed among the options.