Questions: 1-Var-Stats x̄=78.4285714286 Σx=549 Σx^2=43101 Sx=2.69920623253 σx=2.49897938351 n=7 min X=75 Q1=76 Med^2=79 Q3=80 max=83

Transcript text: \[ \begin{array}{l} \text { 1-Var-Stats } \\ \bar{x}=78.4285714286 \\ \Sigma x=549 \\ \Sigma x^{2}=43101 \\ S x=2.69920623253 \\ \sigma x=2.49897938351 \\ n=7 \\ \min \mathrm{X}=75 \\ \mathrm{Q}_{1}=76 \\ \mathrm{Med}^{2}=79 \\ \mathrm{Q}_{3}=80 \\ \max =83 \end{array} \]

Solution

Solution Steps

To solve the given problem, we need to understand the provided statistical data and use it to answer specific questions. Here are the high-level ideas for the first three questions:

Calculate the mean (\(\bar{x}\)): The mean is already provided as 78.4285714286.
Calculate the sum of the data (\(\Sigma x\)): The sum of the data is given as 549.
Calculate the sum of the squares of the data (\(\Sigma x^2\)): The sum of the squares of the data is given as 43101.

We will use Python to verify these values and perform any additional calculations if needed.

Step 1: Verify the Mean

The mean (\(\bar{x}\)) is calculated using the formula: \[ \bar{x} = \frac{\Sigma x}{n} \] Given: \[ \Sigma x = 549, \quad n = 7 \] \[ \bar{x} = \frac{549}{7} = 78.4286 \] The calculated mean matches the provided mean of 78.4286.

Step 2: Verify the Sum of the Data

The sum of the data (\(\Sigma x\)) is given as: \[ \Sigma x = 549 \] This value is directly provided and does not require further calculation.

Step 3: Verify the Sum of the Squares of the Data

The sum of the squares of the data (\(\Sigma x^2\)) is given as: \[ \Sigma x^2 = 43101 \] This value is directly provided and does not require further calculation.