Calculate the standard deviation of a sample for which $n = 6 , \sum x ^ { 2 } = 830 , \sum x = 60$
A) 6.78
B) 6.19
C) 46.00
D) 164.00

Question

Quizplus · Accepted Answer

The standard deviation of a sample is calculated using the formula: $s = \sqrt{\frac{1}{n-1} \left( \sum x^2 - \frac{(\sum x)^2}{n} \right)}$. Substituting the given values, $n = 6$, $\sum x^2 = 830$, and $\sum x = 60$, we get $s = \sqrt{\frac{1}{6-1} \left( 830 - \frac{(60)^2}{6} \right)} = \sqrt{\frac{1}{5} \left( 830 - 600 \right)} = \sqrt{\frac{230}{5}} = \sqrt{46} \approx 6.78$.

Calculate the Standard Deviation of a Sample for Which n=6,∑x2=830,∑x=60n = 6 , \sum x ^ { 2 } = 830 , \sum x = 60n=6,∑x2=830,∑x=60

Calculate the Standard Deviation of a Sample for Which $n = 6 , \sum x ^ { 2 } = 830 , \sum x = 60$