Question

See the image for the information. I have done portions a, b and c but need help with d

Answer 1

d.

The standard deviation for a data set is given by the next formula:

`\sigma=\sqrt[]{\frac{\Sigma(x-x^-)^2_{}}{n}}`

Where n represents the number of data points and x⁻ represents the mean.

Let's check the mean:

`M=(15+27+28+34+42+52)/(6)=(198)/(6)=33`

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:

`\sigma=\sqrt[]{\frac{\Sigma(x-x^-)^2_{}}{n}}`

Where the sum (x-mean)^2. = 828 and n = 6( total number of data points)

`\sigma=\sqrt[]{\frac{828^{}_{}}{6}}`

Hence, the standard deviation is given by:

`\sigma=11.74734012`