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Sagot :
The standard deviation is approximately 1.825
The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
A random variable, sample, statistical population, data set, or probability distribution's standard deviation is equal to the square root of its variance. Although less robust in practice, it is algebraically easier than the average absolute deviation.
The standard deviation is calculated by the formula :
[tex]{\displaystyle \sigma={\sqrt {{\frac {1}{N}}\sum _{i=1}^{N}\left(x_{i}-{\mu }\right)^{2}}}}[/tex]
where N= n-1(n=size of sample) , [tex]\mu[/tex]= mean of the data , [tex]x_i[/tex]= each data value.
Now the given data for the question are {6,5,9,8}
mean of the data ([tex]\mu[/tex])=(6+5+9+8)÷4=28÷4=7
Standard deviation:
[tex]{\displaystyle \sigma ={\sqrt{{\frac {(6-7 )^{2}+(5-7 )^{2}+(9-7 )^{2}+(8-7 )^{2}}{N}}}}[/tex]
[tex]{\displaystyle \sigma ={\sqrt{{\frac {(-1 )^{2}+(-2)^{2}+(2)^{2}+(1 )^{2}}{N}}}}\\[/tex]
[tex]{\displaystyle \sigma =\sqrt{\frac{1+4+4+1}{4-1}}\\[/tex]
[tex]{\displaystyle \sigma =\sqrt{\frac{10}{3}}\\[/tex]
[tex]{\displaystyle \sigma =\sqrt{1.333}[/tex]
[tex]{\displaystyle \sigma =1.825[/tex]
The standard deviation is approximately 1.825.
To learn more about standard deviation visit:
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