Noise levels at 5 volcanoes were measured in decibels yielding the following data:
\[
108,133,140,129,136
\]

Construct the $98 \%$ confidence interval for the mean noise level at such locations. Assume the population is approximately normal.
Step 2 of 3: Caiculate the sample standard deviation for the given sample data. Round your answer to one decimal places.

Answer

Step 1 ：First, calculate the mean of the data. The data is [108, 133, 140, 129, 136]. The mean is calculated as \( \frac{108+133+140+129+136}{5} = 129.2 \)

Step 2 ：Next, for each number in the data, subtract the mean and square the result. This gives us [\( (108-129.2)^2, (133-129.2)^2, (140-129.2)^2, (129-129.2)^2, (136-129.2)^2 \)] which simplifies to [449.44, 14.44, 116.64, 0.04, 46.24]

Step 3 ：Then, find the mean of these squared differences. This is calculated as \( \frac{449.44+14.44+116.64+0.04+46.24}{5} = 125.36 \)

Step 4 ：Finally, take the square root of that mean. This gives us the standard deviation. The standard deviation is \( \sqrt{125.36} = 11.196428001822724 \)

Step 5 ：Round the result to one decimal place as requested. The rounded standard deviation is 11.2

Step 6 ：Final Answer: The sample standard deviation for the given sample data, rounded to one decimal place, is \(\boxed{11.2}\)