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A set of data values is given below:5 6 9 10 8 4a) Calculate the variance;b) Calculate the standard deviation.

User Lloyd Christmas
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1 Answer

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17 votes

The data set is:


\mleft\lbrace5,6,7,10,8,4\mright\rbrace

a) The variance of a data set is given by the formula:


s^2=(1)/(N-1)\sum ^N_(n\mathop=1)(a_n-\operatorname{mean})^2

Where s^2 is the variance and P(a_n) is the probability of the value a_n.

First, we need to calculate the mean of the data set:


\operatorname{mean}=((5+6+9+10+8+4))/(6)=(42)/(6)=7

Now, the variance is:


s^2=(1)/(6)\lbrack(5-7)^2+(6-7)^2+(9-7)^2+(10-7)^2+(8-7)^2+(4-7)^2\rbrack

Then,


s^2=(28)/(5)=5.6

Therefore, the variance is equal to 5.6

b) As for the standard deviation, we simply need to get the square root of the variance. Then,


\text{Standard deviation}=\sqrt[]{s^2}=\sqrt[]{5.6}\approx2.3664

The standard deviation is 2.3664 approximately

User Pedro S Cord
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