IDNLearn.com provides a collaborative environment for finding accurate answers. Our community provides accurate and timely answers to help you understand and solve any issue.
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:
https://brainly.com/question/12402189
#SPJ9
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Discover the answers you need at IDNLearn.com. Thank you for visiting, and we hope to see you again for more solutions.
