Answer:
Explanation:
To calculate the standard deviation, you can follow these steps:
1. Find the mean (average) of the measurements.
2. Subtract the mean from each measurement to find the deviation from the mean for each measurement.
3. Square each deviation.
4. Find the average of the squared deviations.
5. Take the square root of the average from step 4 to get the standard deviation.
Given measurements: {3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0}
1. Mean (\( \bar{X} \)):
\[ \bar{X} = \frac{3.0 + 3.5 + 4.0 + 4.5 + 5.0 + 5.5 + 6.0}{7} = \frac{31.5}{7} \approx 4.5 \]
2. Deviations from the mean:
\[ (-1.5, -1.0, -0.5, 0, 0.5, 1.0, 1.5) \]
3. Squared deviations:
\[ (2.25, 1.0, 0.25, 0, 0.25, 1.0, 2.25) \]
4. Average of squared deviations:
\[ \text{Average} = \frac{2.25 + 1.0 + 0.25 + 0 + 0.25 + 1.0 + 2.25}{7} = \frac{7.0}{7} = 1.0 \]
5. Standard deviation (\( \sigma \)):
\[ \sigma = \sqrt{1.0} = 1.0 \]
Therefore, the correct answer is not provided among the options. It seems there may be an error in the given choices. The correct standard deviation is 1.0.