For two numbers a and b:
⇒ AM = (a + b)/2
EduRev's Tip: AM ≥ GM ≥ HM is always true. They will be equal if all elements are equal to each other. If I have just two values then GM2 = AM*HM
EduRev's Tip: The sum of deviation (D) of each element with respect to the average is 0.
⇒ D = (x1 - xavg) + (x2 - xavg) + (x3 - xavg) ... + (x1 - xavg) = 0
EduRev's Tip: xavg = (xassumed avg + (Deviation/No. of elements))
Important Points: In past year CAT questions, a number of times concepts of age/height/weight and average has been mixed together. Here are some important points to remember.
1. When a person replaces another person then,
(a) If the average is increased, then
(b) If the average is decreased, then
2. When a person joins the group
(a) In case of an increase in average
(b) In case of a decrease in average
In the Arithmetic Progression, there are two cases:
Sum of 1st n consecutive natural numbers = [n(n+1)]/2
Average of 1st n consecutive natural numbers = (n+1)/2