Questions: (sum xi)^2=(1.75+2.76+ldots+1.96)^2=(112.15 times 10.59)^2 We can now use sum xi^2=23.1547,(sum xi)^2=(10.59)^2, and n=5 to calculate s^2. (Round the variance to four decimal places.) s^2 =fracsum xi^2-frac(sum xi)^2nn-1 = frac23.1547-frac(10.59)^25square x = square

(sum xi)^2=(1.75+2.76+ldots+1.96)^2=(112.15 times 10.59)^2

We can now use sum xi^2=23.1547,(sum xi)^2=(10.59)^2, and n=5 to calculate s^2. (Round the variance to four decimal places.)

s^2 =fracsum xi^2-frac(sum xi)^2nn-1
= frac23.1547-frac(10.59)^25square x
= square
Transcript text: \[ \left(\sum x_{i}\right)^{2}=(1.75+2.76+\ldots+1.96)^{2}=(112.15 \times 10.59)^{2} \] We can now use $\sum x_{i}^{2}=23.1547,\left(\sum x_{i}\right)^{2}=(10.59)^{2}$, and $n=5$ to calculate $s^{2}$. (Round the variance to four decimal places.) \[ \begin{aligned} s^{2} & =\frac{\sum x_{i}^{2}-\frac{\left(\sum x_{i}\right)^{2}}{n}}{n-1} \\ & =\frac{23.1547-\frac{(10.59)^{2}}{5}}{\square x} \\ & =\square \end{aligned} \]
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Solution

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Solution Steps

To calculate the variance \( s^2 \), we need to use the formula for variance of a sample:

\[ s^2 = \frac{\sum x_{i}^{2} - \frac{(\sum x_{i})^{2}}{n}}{n-1} \]

Given:

  • \(\sum x_{i}^{2} = 23.1547\)
  • \((\sum x_{i})^{2} = (10.59)^{2}\)
  • \(n = 5\)

We will substitute these values into the formula to compute the variance.

Step 1: Identify the Given Values

We are given the following values:

  • \(\sum x_{i}^{2} = 23.1547\)
  • \((\sum x_{i})^{2} = (10.59)^{2}\)
  • \(n = 5\)
Step 2: Apply the Variance Formula

The formula for the variance of a sample is:

\[ s^2 = \frac{\sum x_{i}^{2} - \frac{(\sum x_{i})^{2}}{n}}{n-1} \]

Substitute the given values into the formula:

\[ s^2 = \frac{23.1547 - \frac{(10.59)^2}{5}}{5-1} \]

Step 3: Perform the Calculations

Calculate the squared sum of \(x_i\):

\[ (10.59)^2 = 112.1481 \]

Substitute back into the formula:

\[ s^2 = \frac{23.1547 - \frac{112.1481}{5}}{4} \]

Calculate the expression:

\[ s^2 = \frac{23.1547 - 22.42962}{4} = \frac{0.72508}{4} = 0.18127 \]

Final Answer

\(\boxed{s^2 = 0.1813}\)

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