Problem 6SE

There are 15 numbers on a list, and the smallest number 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?

Solution 6SE

Step1 of 3:

We have sample size N = 15 and mean

Total number of observations X’s is 15

The smallest number on a list X is changed from 12.9 to 1.29.

We need to find,

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?

Step2 of 3:

a).

Yes , It is possible to determine by how much the mean changes and the value of mean after changing value from 12.9 to 1.29 is given by

Sample mean is calculated by using the formula

Where,

x = random variable

= mean

N = sample size.

Consider,

New mean

=

=

Therefore, the mean decreases to 0.779.

b).

No, it is not possible to determine the value of the mean after the change because we dont know the value of mean before the mean.

Step3 of 3:

c).

Yes, It is possible to determine by how much the median changes because we have 15 numbers in a data set and doesn’t effect the median so the median didn’t change.

d).

No it is impossible to determine how much the standard deviation changes .