Find the standard deviation of a series of ACT scores listed below.
\[
17,20,26,24,23
\]
The standard deviation is
(Type an integer or decimal rounded to the nearest hundredth as needed.)
Answer
Final Answer: The standard deviation of the ACT scores is \(\boxed{3.16}\)
Step 1 ：Calculate the mean (average) of the numbers: \(\frac{17+20+26+24+23}{5} = 22.0\)
Step 2 ：Subtract the mean from each number and square the result: \((17-22)^2 = 25.0, (20-22)^2 = 4.0, (26-22)^2 = 16.0, (24-22)^2 = 4.0, (23-22)^2 = 1.0\)
Step 3 ：Calculate the mean of these squared differences: \(\frac{25.0+4.0+16.0+4.0+1.0}{5} = 10.0\)
Step 4 ：Take the square root of the result from step 3: \(\sqrt{10.0} = 3.1622776601683795\)
Step 5 ：Final Answer: The standard deviation of the ACT scores is \(\boxed{3.16}\)
