d.
The standard deviation for a data set is given by the next formula:
[tex]\sigma=\sqrt[]{\frac{\Sigma(x-x^-)^2_{}}{n}}[/tex]
Where n represents the number of data points and x⁻ represents the mean.
Let's check the mean:
[tex]M=\frac{15+27+28+34+42+52}{6}=\frac{198}{6}=33[/tex]
Hence, the mean is 33.
Now, the table for part b:
Where the third column represents the subtraction between x and the means. Also, the fourth column represents the (x-mean)^2.
Where the sum is equal to 828.
Now, we can replace the given values on the standard deviation:
[tex]\sigma=\sqrt[]{\frac{\Sigma(x-x^-)^2_{}}{n}}[/tex]
Where the sum (x-mean)^2. = 828 and n = 6( total number of data points)
[tex]\sigma=\sqrt[]{\frac{828^{}_{}}{6}}[/tex]
Hence, the standard deviation is given by:
[tex]\sigma=11.74734012[/tex]
