How to Solve Problems on Averages

Arithmetic Average

The formula for calculating average is :                                                                                                                                Average = (x1 + x2 + x3 +x4 +x5 + x6 + ... + xn)/n  where,                 n is the number of  quantities                 x1 is the value of first quantity, x2 is the value of second quantity and so on.                              Example: There are seven boxes having weight of 7, 6 , 8, 5, 4 , 6 ,8. Calculate                the average of all the boxes. Solution: Using the above formula, we have seven boxes, therefore n =7               and x1 = 7, x2 = 6 and so on                put the values in the above formula to get                                    average =  ( 7+ 6 + 8 + 5 +4 +6 +8)/7 = 44/7 = 6.28 approx.

Weighted Average 

In case of weighted average we assign different weights to each quantity and then calculate their average. Formula for weighted average is    Average (weighted) =  (w1x1 + w2x2 + w3x3 + .... + wnxn)/(w1 + w2 + w3 +.. + wn)      Where,            w1,w2,w3....wn are the weights of x1,x2,x3,...xn quantities. Example: A student scored 60, 80 and 70 in Physics, chemistry and math. If the college assigns a weight of 3 to physics, 1 to chemistry and 2 to math for admission to the physics course, then calculate the weighted average of the student. Solution: Here,  Weights of marks in physics, chemistry and math are 30, 40 and 80 respectively. Therefore using the formula for the weighted average, we have,                                   weighted Average = (3x60+ 1x80 + 2x70)/(3 + 1 + 2 )                                                    = (180 + 80 + 140)/(6)                                                    = 66.67 and an arithmetic average would have been                                                    = (210)/3= 71 Comparison between Weighted average and arithmetic average: The weighted average calculated in this case is less than the arithmetic average because of the weight attached to the various subjects. Since Maximum weight is attached to physics, and the student has scored less mark in physics, this will pull down the average. Take another scenario where admission is sought in chemistry course and the weight attached are as: Math          =  1 Physics       =  2 chemistry   = 3 Then the weighted average would be  = ( 120 + 240 + 70)/6 =  71.67 Now weighted average has come out to be greater than arithmetic average because of the weight assigned to chemistry and the higher marks in chemistry has pull UP the weighted average.

Try out:  



Solved Problems on averages
 

and :

Solved Problems on unitary methods
 
Solved problems on percentages