Average

Average

In this post, We will learn about average. 

Average of any collection of data is the sum of data divide by number of data.

Average = (Sum of observations / Number of observations)

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problems

The arithmetic mean of x, y and z is 80, and that of x, y, z, u and v is 75, where u=(x+y)/2 and v=(y+z)/2. If x ≥ z, then the minimum possible value of x is (CAT 2018)

As specified in the question mean of x and y and z is 80
x+y+z=3*80
mean of x, y, z,u,v is 75
x+y+z+u+v=75*5
2u=x+y
2v=y+z
x+y+z+((x+y+y+z)/2)=75*5
y+3(x+y+z)=75*10
y=750-720
y=30
since x+y+z=240
y=30
so x+z=210
since x>=z
so minimum value of x=210/2 = 105

Problem2: In first 5 inings sehwag has scored at average of 40. In sixth ining He had scored 52 what is His average after 6th ining.

one simple approach is getting total score divided by no of inings
total score= (40*5+52)
avg after 6th ining: 252/6=42
anoter approach will be get difference between current score and previous average and eaually distribute that difference by total no of measurements after new record added.
52-40=12
now 12 distributed bw 6 will be 2.
so new avg = old avg + 2
so new avg = 40 + 2=42