Multiple Choice
Given the data set , , , , , , , , what is the variance and what is the standard deviation, rounded to the nearest whole number?
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3. Describing Data Numerically
Standard Deviation
Multiple Choice
What is the standard deviation of the following sample data: , , , , ?
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Verified step by step guidance1
First, calculate the sample mean \( \bar{x} \) by summing all the data points and dividing by the number of data points. For the data set \( 2, 6, 2, 0, 5 \), the formula is:
\[ \bar{x} = \frac{2 + 6 + 2 + 0 + 5}{5} \]
Next, find the squared differences between each data point and the sample mean. For each data point \( x_i \), compute:
\[ (x_i - \bar{x})^2 \]
Then, sum all the squared differences obtained in the previous step:
\[ \sum_{i=1}^{n} (x_i - \bar{x})^2 \]
Since this is a sample, calculate the sample variance by dividing the sum of squared differences by \( n - 1 \), where \( n \) is the number of data points:
\[ s^2 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n - 1} \]
Finally, find the sample standard deviation by taking the square root of the sample variance:
\[ s = \sqrt{s^2} \]
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