Given:
Data x: 24, 28, 26, 30, 32
n = 5
Asked: What is the standard deviation of the population?
Formula:
[tex]\text{standard deviation = }\sqrt[]{\frac{\sum ^{}_{}(x-\bar{x})^2}{n}}[/tex]Solution:
Step 1: We will get the average of the data given.
NOTE: Bar x is also the mean or the average.
[tex]\begin{gathered} \bar{x}\text{ = }\frac{24+28+26+30+32}{5}\text{ } \\ \bar{x}=\text{ 28} \end{gathered}[/tex]Step 2: We will subtract the mean from each number.
Step 3: We will square the differences and get the summation.
Step 4: We will substitute the acquired values to find the standard deviation using the formula above.
[tex]\begin{gathered} \text{standard deviation = }\sqrt[]{\frac{\sum ^{}_{}(x-\bar{x})^2}{n}} \\ \text{standard deviation = }\sqrt[]{\frac{40^{}}{5}}\text{ } \\ \text{standard deviation = 2}\sqrt[]{2}\text{ = }2.828427125 \end{gathered}[/tex]ANSWER: standard deviation = 2.83 (Rounded off to 2 decimal places)
