A set of data consists of the following 9 numbers: 0, 2, 4, 6, and 8. Which two numbers, if added to create a set of 7 numbers, will result in a new standard deviation that is close to the standard deviation for the original 5 numbers? Choose the most appropriate option:	A) -1 and 9	B) 4 and 4	C) 3 and 5	D) 2 and 6	E) 0 and 8
If you are in for some calculations , this is how I got to it   mean = 4   sd = \sqrt{8} = 2.8   Expected values for the SD to not change are - One value below SD from mean is (4 - 2.8)= 
<gadget id="calculator">(4 - 2.8)</gadget>
<output>1.2</output>
1.2 , and one value above SD is (4 + 2.8)= 
<gadget id="calculator">(4 + 2.8)</gadget>
<output>6.8</output>
6.8   This would mean , adding 1.2 ans 6.8 would have no impact on the SD . SD remains the same when these two numbers are added. Now for SD to change the least , we need to add two values that are closest to these two values.   Hence any two values that are closest to 1.2 and 6.8 would change the SD , the least.   1. -1 , 9   distance between (1,9) and (1.2 and 6.8) is 2.2 and 2.2   2. 4 , 4   distance etween (4,4) and (1.2 , 6.8) is 2.8 and 2.8   3. 3 , 5   Distance is - 1.8 and 1.8   4. 2 , 6   Distance is - 0.8 and 0.8   5. 0 , 8   Distnace is - 1.2 and 1.2   Hence from above , we see that adding -1 and 9 , results in a value that would change the SD to the least. Hence -1 and 9
<result>A</result>
A set of data consists of the following 9 numbers: 0, 2, 4, 6, and 8. Which two numbers, if added to create a set of 7 numbers, will result in a new standard deviation that is close to the standard deviation for the original 5 numbers?