Question

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

Answer 1

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:

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

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:

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

Now, the variance is:

$s^2=\frac{1}{6}\lbrack(5-7)^2+(6-7)^2+(9-7)^2+(10-7)^2+(8-7)^2+(4-7)^2\rbrack$

Then,

$s^2=\frac{28}{5}=5.6$

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