The standard deviation of the data set 4, 6, 2, and 5 is

The standard deviation of a data set is given as:

$\sigma =\sqrt{\frac{1}{N}\times \sum _{i=1}^N(x_i-\bar{x}{)}^2}$

where:

$N$ - number of data;

$\bar{x}$ - mean value

$x_i$ - data in data set

To calculate the deviation we can use the following algorythm:

1. Calculate mean $\bar{x}$

2. Calculate $(x_i-\bar{x}{)}^2$ for all $i$

3. Add all values calculated in $2$

4. Divide the sum by N

5. Get square root to calculate the deviation.

Here we have:

1. $\bar{x}$$=\frac{4+6+2+5}{4}=\frac{17}{4}=4.25$

2. $(2-4.25{)}^2=(-2.25{)}^2\approx 5$

    $(4-4.25{)}^2=(-0.25{)}^2\approx 0.0625$

    $(5-4.25{)}^2=(1.25{)}^2\approx 1.6$

    $(6-4.25{)}^2=(2.25{)}^2\approx 5$

3. Sum is $5+0.0625+1.6+5\approx 12$

4. $12÷4.25\approx 2.8$

5. $\sigma =\sqrt{2.8}\approx 1.67$