Answer :
Answer:
The standard deviation of the data set is [tex]\sigma = 12.7906[/tex].
Step-by-step explanation:
The Standard Deviation is a measure of how spread out numbers are. Its symbol is σ (the greek letter sigma)
To find the standard deviation of the following data set
[tex]\begin{array}{cccccccc}83&87&90&92&93&100&104&111\\115&121&&&&&&\end{array}[/tex]
we use the following formula
[tex]\sigma = \sqrt{ \frac{ \sum{\left(x_i - \overline{X}\right)^2 }}{n-1} }[/tex]
Step 1: Find the mean [tex]\left( \overline{X} \right)[/tex].
The mean of a data set is the sum of the terms divided by the total number of terms. Using math notation we have:
[tex]Mean = \frac{Sum ~ of ~ terms}{Number ~ of ~ terms}[/tex]
[tex]Mean = \frac{Sum ~ of ~ terms}{Number ~ of ~ terms}=\frac{83+87+90+92+93+100+104+111+115+121}{10} \\\\Mean = \frac{996}{10} =\frac{498}{5}=99.6[/tex]
Step 2: Create the below table.
Step 3: Find the sum of numbers in the last column to get.
[tex]\sum{\left(x_i - \overline{X}\right)^2} = 1472.4[/tex]
Step 4: Calculate σ using the above formula.
[tex]\sigma = \sqrt{ \frac{ \sum{\left(x_i - \overline{X}\right)^2 }}{n-1} } = \sqrt{ \frac{ 1472.4 }{ 10 - 1} } \approx 12.7906[/tex]
Answer:
B
Step-by-step explanation:
range = biggest - smallest
121 - 83 = 38
range = 38