There are 15 numbers on a list, and the mean is 25. The smallest number on the list is changed from 12.9 to 1.29.

a. Is it possible to determine by how much the mean changes? If so, by how much does it change?

b. Is it possible to determine the value of the mean after the change? If so, what is the value?

c. Is it possible to determine by how much the median changes? If so, by how much does it change?

d. Is it possible to determine by how much the standard deviation changes? If so, by how much does it change?

Answer :

Step 1 of 4 :

Given,

We have the list of 15 members, mean is 25. The smallest number on the list is changed from 12.9 to 1.29.

The claim is to find how much the mean is changingIt is possible to determine the how much mean changes.

Mean after the change =

= +

= - 0.774

The mean value is negative.

The mean decreases by 0.774.

Step 2 of 4 :

b)

The claim is to determine the value of mean after the change.

Yes, it is possible to determine the value of mean after the change.

Mean =

Where, mean = 25 and n = 15

= (25) (15)

= 375

The mean after change is

Mean = 375 -12.9 + 1.29

= 363.39

The mean after the change is 363.39

Step 3 of 4 :

c)

The claim is to determine whether the median changes or not.

No, it is not possible to determine how much the data changes.

Median = middle most value of the data when it is arranged in ascending order.

In this data the minimum value is replaced.

Hence, median does not change.