1. ## standard deviation changes

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?

I have problem with part d , i dont have the ans .

So , we need to compute the new ∑x and ∑(x^2 ) , the new ∑x = old ∑x + 1.29 -12.9

the new ∑(x^2 ) = old ∑(x^2 ) - (12.9^2) + (1.29^2) ...
However , the old ∑x and ∑(x^2 )are not provided , so we cant calculate the changes

Correct me if i am wrong

2. ## Re: standard deviation changes

A) by $\dfrac{1.29-12.9}{15}$
B) $\dfrac{25\cdot 15+1.29-12.9}{15}$
C) not possible
D) not possible

3. ## Re: standard deviation changes

Originally Posted by SlipEternal
A) by $\dfrac{1.29-12.9}{15}$
B) $\dfrac{25\cdot 15+1.29-12.9}{15}$
C) not possible
D) not possible
I think the median is unchanged , since the total number of elements is unchanged .

4. ## Re: standard deviation changes

Originally Posted by xl5899
I think the median is unchanged , since the total number of elements is unchanged .
Example:
12.9, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 37.1 - Median = 25. After change in datapoint, Median = 25 (Median Unchanged)
0, 0, 0, 0, 0, 0, 0, 12.9, 51, 51.85, 51.85, 51.85, 51.85, 51.85, 51.85 - Median = 12.9. After change in datapoint, Median = 1.29 (Median Changed!!!).

The median can definitely change. So long as I choose a sum that adds to 375 and includes one datapoint that is 12.9, I can make the median start as any number and end as any number I choose.

5. ## Re: standard deviation changes

The original problem said "The smallest number on the list is changed from 12.9 to 1.29". In your example, the "smallest number on the list" is 0, not 12.9, and does not change. Your example is not valid.

6. ## Re: standard deviation changes

Originally Posted by HallsofIvy
The original problem said "The smallest number on the list is changed from 12.9 to 1.29". In your example, the "smallest number on the list" is 0, not 12.9, and does not change. Your example is not valid.
Good point. I did miss that. Thank you. The OP is correct that the median cannot change.