Questions: Find the sample variance and standard deviation. 18,12,5,8,11 Choose the correct answer below. Fill in the answer box to complete your choice. (Type an integer or a decimal. Round to one decimal place as needed.) A. σ²= B. s²=

Find the sample variance and standard deviation. 18,12,5,8,11 Choose the correct answer below. Fill in the answer box to complete your choice. (Type an integer or a decimal. Round to one decimal place as needed.) A. σ²= B. s²=
Transcript text: Find the sample variance and standard deviation. \[ 18,12,5,8,11 \] Choose the correct answer below. Fill in the answer box to complete your choice. (Type an integer or a decimal. Round to one decimal place as needed.) A. $\sigma^{2}=$ $\square$ B. $s^{2}=$ $\square$
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Solution

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Solution Steps

Step 1: Determine if the calculation is for a population or a sample

The calculation is for a sample.

Step 2: Calculate the mean

The mean (\(\mu\) or \(\bar{x}\)) is calculated as \(\frac{1}{5}\sum_{i=1}^{5}x_i\), which equals 10.8.

Step 3: Calculate the variance

The sample variance (\(s^2\)) is calculated as \(\frac{1}{5-1}\sum_{i=1}^{5}(x_i - \bar{x})^2\), which equals 23.7.

Step 4: Calculate the standard deviation

The sample standard deviation (\(s\)) is the square root of \(s^2\), which equals 4.9.

Final Answer:

The sample variance is 23.7 and the sample standard deviation is 4.9.

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