Answer:
The sample standard deviation is 393.99
Step-by-step explanation:
The standard deviation of a sample can be calculated using the following formula:
[tex]s=\sqrt[ ]{\frac{1}{N-1} \sum_{i=1}^{N}(x_{i}-{\displaystyle \textstyle {\bar {x}}}) ^{2} }[/tex]
Where:
[tex]s=[/tex] Sample standart deviation
[tex]N=[/tex] Number of observations in the sample
[tex]{\displaystyle \textstyle {\bar {x}}}=[/tex] Mean value of the sample
and [tex]\sum_{i=1}^{N}(x_{i}-{\displaystyle \textstyle {\bar {x}}}) ^{2} }[/tex] simbolizes the addition of the square of the difference between each observation and the mean value of the sample.
Let's start calculating the mean value:
[tex]\bar {x}=\frac{1}{N} \sum_{i=1}^{N}x_{i}[/tex]
[tex]\bar {x}=\frac{1}{15}*(180+1600+90+140+50+260+400+90+380+110+10+60+20+340+80)[/tex]
[tex]\bar {x}=\frac{1}{15}*(3810)[/tex]
[tex]\bar {x}=254[/tex]
Now, let's calculate the summation:
[tex]\sum_{i=1}^{N}(x_{i}-\bar {x}) ^{2} }=(180-254)^2+(1600-254)^2+(90-254)^2+...+(80-254)^2[/tex]
[tex]\sum_{i=1}^{N}(x_{i}-\bar {x}) ^{2} }=2173160[/tex]
So, now we can calculate the standart deviation:
[tex]s=\sqrt[ ]{\frac{1}{N-1} \sum_{i=1}^{N}(x_{i}-{\displaystyle \textstyle {\bar {x}}}) ^{2} }[/tex]
[tex]s=\sqrt[ ]{\frac{1}{15-1}*(2173160)}[/tex]
[tex]s=\sqrt[ ]{\frac{2173160}{14}}[/tex]
[tex]s=393.99[/tex]
The sample standard deviation is 393.99
