nav.adi wrote:And we can maximize the range if the set is
I did-not understand how you reached the above..can you please explain
This is the concept for maximizing and minimizing . We are given that the mean in 55 .
Note : we have 5 numbers in the set so 55 must be the 3rd element in the set . To find the max range we would need the smallest element to be repeated max times .
We dont know the 2 nd and 4 th element in the set .
5a+130=275 (from Eq.1)
5a= 145 ---> a=29
Lets suppose we consider 2 nd element to be say 33 (we need to consider this element to be smaller or equal to mean.)
And the 4 th element to be say 65(this value has to be equal to or greater than the mean) .
See what effect it has on Eq 1 .
a + 33 + 55 + 65 + 3a+20 = 275
4a + 173 = 275
a = 25.5
so the range = 2a + 20 = 71 . That is much smaller than 78 .
Now if we decrease the values of 2 nd and 4 th elements we would max value for a and thus the max value for the range .
Because the only variable on which the value of range depends is a (2a + 20) . So max the value of a max is the range .
Having said that the thing to note is the value of 2 nd element can not be lower than a or greater than mean , similarly the value of 4 th element can not be more than 3a+20 and less than mean . Because all elements in the set are arranged in ascending order .
Hope this clear things up a bit .