Questions: Consider the following data: 9,11,8,14,7,5 Step 2 of 3: Calculate the value of the sample standard deviation. Round your answer to one decimal place.

Consider the following data:
9,11,8,14,7,5
Step 2 of 3: Calculate the value of the sample standard deviation. Round your answer to one decimal place.

Transcript text: Consider the following data: \[ 9,11,8,14,7,5 \] Step 2 of 3: Calculate the value of the sample standard deviation. Round your answer to one decimal place.

Solution

Solution Steps

Step 1: Calculate the sample mean (\(\bar{x}\))

To find the sample mean, sum all the data points and divide by the number of data points (n=6). \[\bar{x} = \frac{1}{6} \sum_{i=1}^{6} x_i = 9\]

Step 2: Calculate the variance

Subtract the mean from each data point, square the result, sum all those squared differences, and then divide by \(n-1\). \[\text{Variance} = \frac{1}{6-1} \sum_{i=1}^{6} (x_i - \bar{x})^2\]

Step 3: Calculate the sample standard deviation

Take the square root of the variance. \[s = \sqrt{\text{Variance}} = 3.2\]