Questions: What are the sample standard deviation for process 1 and 2?

Solution Steps

To find the sample standard deviation for two processes, we need to:

1. Collect the data points for each process.
2. Calculate the mean (average) of the data points for each process.
3. Compute the squared differences from the mean for each data point.
4. Find the average of these squared differences.
5. Take the square root of this average to get the sample standard deviation.

We need to calculate the sample standard deviation for two different processes. The sample standard deviation is a measure of the amount of variation or dispersion in a set of values.

The formula for the sample standard deviation \( s \) is: \[ s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2} \] where:

• \( n \) is the number of observations,
• \( x_i \) are the individual observations,
• \( \bar{x} \) is the sample mean.

Assume the data for process 1 is \( x_1, x_2, \ldots, x_n \).

\[ \bar{x}_1 = \frac{1}{n} \sum_{i=1}^{n} x_i \]

\[ s_1 = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x}_1)^2} \]

Assume the data for process 2 is \( y_1, y_2, \ldots, y_m \).

\[ \bar{x}_2 = \frac{1}{m} \sum_{i=1}^{m} y_i \]

\[ s_2 = \sqrt{\frac{1}{n-1} \sum_{i=1}^{m} (y_i - \bar{x}_2)^2} \]

Final Answer