2022-01-10

The standard deviation of the data set 4, 6, 2, and 5 is star233

Expert

The standard deviation of a data set is given as:

$\sigma =\sqrt{\frac{1}{N}×\sum _{i=1}^{N}\left({x}_{i}-\stackrel{―}{x}{\right)}^{2}}$

where:

$N$ - number of data;

$\stackrel{―}{x}$ - mean value

${x}_{i}$ - data in data set

To calculate the deviation we can use the following algorythm:

1. Calculate mean $\stackrel{―}{x}$

2. Calculate $\left({x}_{i}-\stackrel{―}{x}{\right)}^{2}$ 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. $\stackrel{―}{x}$$=\frac{4+6+2+5}{4}=\frac{17}{4}=4.25$

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

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

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

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

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

4. $12÷4.25\approx 2.8$

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

Do you have a similar question?