Questions: Consider the following data: 9, -5, 9, -5, 2, 9, -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, -5, 9, -5, 2, 9, -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: \[ 9,-5,9,-5,2,9,-5 \] Step 2 of 3: Calculate the value of the sample standard deviation. Round your answer to one decimal place. AnswerHow to enter your answer (opens in new window) 2 Points

Solution

Solution Steps

Step 1: Calculate the sample mean

The sample mean (\(\bar{x}\)) is calculated as \(\bar{x} = \frac{1}{7}\sum_{i=1}^{7}x_i\), which equals 2.

Step 2: Calculate the squared differences from the mean

For each observation \(x_i\) in the dataset, calculate the squared difference from the mean \((x_i - \bar{x})^2\). The squared differences are: [49, 49, 49, 49, 0, 49, 49].

Step 3: Sum up all the squared differences

The total squared deviation from the mean is \(\sum_{i=1}^{7}(x_i - \bar{x})^2\), which equals 294.

Step 4: Divide the total squared deviation by \(n-1\)

This gives us the variance: \(\frac{1}{6}\sum_{i=1}^{7}(x_i - \bar{x})^2\), which equals 49.

Step 5: Take the square root of the variance

This gives us the sample standard deviation: \(\sqrt{\frac{1}{6}\sum_{i=1}^{7}(x_i - \bar{x})^2}\), which equals 7.