Question

Find the measure of center that best represents each set data round to the nearest tenth if necessary number of parking spaces used: 46,39,40,45,44,68,51

Answer 1

`\bar X = 47.57`

Now we can calculate the standard deviation :

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

And replacing we got:

`s = 9.846`

We can see the the standard deviation is lower than the sample mean and then we can conclude that the sample mean would be a good decription for a measure of center.

Other reason to no use the median is because we don't have enough sample size to assume that this measure represent very well the measure of center.

Explanation:

For this case we have the following data:

46,39,40,45,44,68,51

We can begin calculating the sample mean with this formula:

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

And replacing we got:

`\bar X = 47.57`

Now we can calculate the standard deviation :

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

And replacing we got:

`s = 9.846`

We can see the the standard deviation is lower than the sample mean and then we can conclude that the sample mean would be a good decription for a measure of center.

Other reason to no use the median is because we don't have enough sample size to assume that this measure represent very well the measure of center.