The smallest number on a 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 by how much the median changes? If so, by how much does it change? What if the list consists of only two numbers?

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

Solution 5SE

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 by how much the median changes? If so, by how much does it change? What if the list consists of only two numbers?

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

Step2 of 3:

a).

Sample mean is calculated by using the formula

Where,

x = random variable

= mean

N = sample size

New mean is given by

New mean() =

=

=

=

= 24.226.

Hence,= 24.226.

Therefore, new mean is 24.226.

b).

No, It is not possible to determine by how much the median changes because median is nothing but middle most value in a Ascending ordered data. Here we are changing the smallest value 12.9 to 1.29 so it is not possible to determine by how much the median changes.

Step3 of 3:

c).

Standard deviation is given by

=

= 375

New standard deviation is given by

=

=

= 19.0627

Hence,=19.0627.

Therefore, New standard deviation is 19.0627.

Conclusion:

a).Yes, it possible to determine by how much the mean changes and the new mean is 24.226.

b).No, It is not possible to determine by how much the median changes.

c).Yes, it is possible to determine by how much the standard deviation changes and the new standard deviation is 19.0627.