Problem

Find the standard deviation for the group of data items.
\[
7,8,9,10,11 \text { 무 }
\]

The standard deviation is

Answer

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Answer

Final Answer: The standard deviation for the group of data items is \( \boxed{1.4142135623730951} \)

Steps

Step 1 :Find the mean (average) of the data set: \( \frac{7+8+9+10+11}{5} = 9.0 \)

Step 2 :Subtract the mean from each data point and square the result: \( (7-9)^2, (8-9)^2, (9-9)^2, (10-9)^2, (11-9)^2 \) which results in \( 4, 1, 0, 1, 4 \)

Step 3 :Find the mean of these squared differences: \( \frac{4+1+0+1+4}{5} = 2.0 \)

Step 4 :Take the square root of the result: \( \sqrt{2.0} = 1.4142135623730951 \)

Step 5 :Final Answer: The standard deviation for the group of data items is \( \boxed{1.4142135623730951} \)

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