Question : Find the standard deviation of the following data (rounded off to two decimal places).
5, 3, 4, 7
Option 1: 1.48
Option 2: 3.21
Option 3: 4.12
Option 4: 2.45
Correct Answer: 1.48
Solution :
Standard deviation of 5, 3, 4, 7
= $\sqrt{\frac{\sum {x_i}^2}{n}-(\frac{\sum x_i}{n})^2}$
where $x_i$ are the numbers and $n$ is the count of numbers.
= $\sqrt{\frac{5^2+3^2+4^2+7^2}{4}-(\frac{5+3+4+7)}{4})^2}$
= $\sqrt{\frac{99}{4}-\frac{361}{16}}$
= $\sqrt{\frac{35}{16}}$
= 1.48
Hence, the correct answer is 1.48.
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