Question

A group of kids just finished trick-or-treating. The number of pieces of candy collected by each of the 5 kids

is listed below.
31, 33, 36, 41, 34
Find the standard deviation of the data set.
Round your answer to the nearest hundredth.​

Answer 1

`s = \sqrt{(\sum_(i=1)^n (X_i -\bar X)^2)/(n-1)}`

`s =\sqrt{((31-35)^2 +(33-35)^2 +(36-35)^2 +(41-35)^2 +(34-35)^2)/(5-1)} =3.808`

And the answer for this case would be :

`s= 3.81` after round the value

Explanation:

We have the following data set given:

31, 33, 36, 41, 34

If we want to find the standard deviation we need to find first the sample mean with this formula:

`\bar X = (\sum_(i=1)^n X_i)/(n)`

And replacing we got:

`\bar X = (31+33+36+41+34)/(5)= (175)/(5)= 35`

Now we can find the sampel deviation with this formula:

`s = \sqrt{(\sum_(i=1)^n (X_i -\bar X)^2)/(n-1)}`

And replacing we got:

`s =\sqrt{((31-35)^2 +(33-35)^2 +(36-35)^2 +(41-35)^2 +(34-35)^2)/(5-1)} =3.808`

And the answer for this case would be :

`s= 3.81` after round the value