Questions: For the data set, calculate Σx, Σx², and (Σx)². -8,-1,3,8,1,7,-7,9,4 Σx = Enter an exact number. Σx² (Σx)² =

Transcript text: For the data set, calculate $\Sigma x, \Sigma x^{2}$, and $(\Sigma x)^{2}$. \[ \begin{aligned} & -8,-1,3,8,1,7,-7,9,4 \\ \Sigma x & =\frac{1}{1} \begin{array}{l} \text { Enter an exact number. } \end{array} \\ \Sigma x^{2} & \\ (\Sigma x)^{2} & =\square \end{aligned} \]

Solution

Solution Steps

To solve the problem, we need to perform the following steps:

Calculate the sum of the data set, denoted as $\Sigma x$.
Calculate the sum of the squares of each element in the data set, denoted as $\Sigma x^2$.
Calculate the square of the sum of the data set, denoted as $(\Sigma x)^2$.

Step 1: Calculate $ \Sigma x $

The sum of the data set is calculated as follows: \[ \Sigma x = -8 + (-1) + 3 + 8 + 1 + 7 + (-7) + 9 + 4 = 16 \]

Step 2: Calculate $ \Sigma x^2 $

The sum of the squares of each element in the data set is calculated as follows: \[ \Sigma x^2 = (-8)^2 + (-1)^2 + 3^2 + 8^2 + 1^2 + 7^2 + (-7)^2 + 9^2 + 4^2 = 64 + 1 + 9 + 64 + 1 + 49 + 49 + 81 + 16 = 334 \]

Step 3: Calculate $ (\Sigma x)^2 $

The square of the sum of the data set is calculated as follows: \[ (\Sigma x)^2 = 16^2 = 256 \]

Final Answer

\[ \Sigma x = 16, \quad \Sigma x^2 = 334, \quad (\Sigma x)^2 = 256 \] Thus, the final boxed answers are: \[ \boxed{\Sigma x = 16}, \quad \boxed{\Sigma x^2 = 334}, \quad \boxed{(\Sigma x)^2 = 256} \]

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!