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

Construct the $98\mathrm{\%}$ 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 $\boxed{{\displaystyle 11.2}}$