Question

Calculate the mean and standard deviation of the data set ...

Answer 1

Mean: 12.9

Standard deviation: 14.8

Explanation:

The mean is calculated adding all of the values and dividing by the number of elements:

`m=(2+3+7+12+1+4+27+49+11)/(9)=(116)/(9)=12.9`

to find the standard deviation, we first find the variance (which is defined as the sum of all the elements subtracting the mean and squared and then dividing by the total amount of elements):

`v=((2-12.9)^2+(3-12.9)^2+(7-12.9)^2+(12-12.9)^2+(1-12.9)^2+(4-12.9)^2+(27-12.9)^2+(49-12.9)^2+(11-12.9)^2)/(9)\\`

`v=(1978.89)/(9)\\`

`v=219.88`

Noe that we have the variance, we can calculate the standard deviation.

The stardard deviation is defined as the squared root of the variance:

`standardDeviation=√(v)`

we substitute the variance:

`standardDeviation=√(219.88) \\standardDeviation=14.8`

Thus, the answer is:

Mean: 12.9

Standard deviation: 14.8