Answer :
Given:
Barista: $12.50,
Lead Barista: $13.75,
Trainee: $11.25,
Shift supervisor: $15,
Barista: $12.50,
Store Manager: $33
Required:
To find the standard deviation and range of the given data.
Explanation:
Standard deviation :
[tex]SD=\sqrt{\sum_^\frac{(x-x1)^2}{n-1}}[/tex]Here x1 is the mean.
Now,
[tex]\begin{gathered} x1=\frac{12.50+13.75+11.25+12.50+33}{4} \\ \\ =\frac{83}{5} \\ \\ =16.6 \end{gathered}[/tex]So,
[tex]\begin{gathered} =(12.5-16.6)^2+(13.75-16.6)^2+(11.25-16.6)^2+(12.5-16.6)^2+(33-16.6)^2 \\ \\ =8.1225+28.6225+268.96 \\ \\ =305.705 \end{gathered}[/tex]Now
[tex]\begin{gathered} SD=\frac{305.705}{5-1} \\ \\ =\frac{305.705}{4} \\ \\ =76.426 \end{gathered}[/tex]Range:
To find the range, order all values in your data set from low to high. Subtract the lowest value from the highest value.
Therefore,
[tex]11.25,12.50,12.50,13.75,33[/tex]The range is
[tex]\begin{gathered} R=33-11.25 \\ \\ =21.75 \end{gathered}[/tex]Final Answer:
Standard deviation = 76.426
Range = 21.75
