Quantitative Aptitude

Averages Mixtures and Alligation-Averages, Mixtures and Alligation

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Averages, Mixtures and Alligation Aptitude basics, practice questions, answers and explanations 
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Important Formula and Equations

  • Average= Sum of observations/ Number of observations
  • The average of odd numbers from  1 to n is    = [Last odd no. + 1]/ 2.
  • The average of even numbers from  1 to n is  = [Last even no. + 2]/2.

 

Name

Equation or description

Arithmetic mean

Median

The middle value that separates the higher half from the lower half of the data set

Geometric median

A rotation invariant extension of the median for points in Rn

Mode

The most frequent value in the data set

Geometric mean

Harmonic mean

Quadratic mean 
(or RMS)

Generalized mean

Weighted mean

Truncated mean

The arithmetic mean of data values after a certain number or proportion of the highest and lowest data values have been discarded

Interquartile mean

A special case of the truncated mean, using the interquartile range

Midrange

Winsorized mean

Similar to the truncated mean, but, rather than deleting the extreme values, they are set equal to the largest and smallest values that remain

Annualization

  • The Average of any number of quantities is sum of their quantities by the number of quantities (n).
    Average=Sum of quantities/n
     
  • If there are two types of items say A and B , A has m number of sub items and B has n number of sum items then the average of A and B is (Am+Bn)/(m+n)
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  • If a vehicle travels from one place to another at a speed of a kmph but returns at the speed of b kmph then its average speed during the whole journey is 2ab/(a+b)  kmph.
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  • Out of three numbers, first number is x times of the second number and y times of the third number. If the average of all the three numbers is z then the first number is   3xyz /(xy+x+y)
                                                                                                              
  • Let the average age of men and women in a town be x years and the average age of women be y years and the average age of men be z years. Then the number of men in that town is   N(x-y)/(z-y)
    (z-y) if N indicates the total number of men and women of the town.              
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  • The average age of N persons is x years. If one new person joins them. Then the average age is increased by y years. Then the age of new comer is x + (1 + N) y years.
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  • The average age of N persons is x years. If M persons joins them, the average age is increased by y years then the average age of newcomers is x+(1+(N/M)) y years
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  • The average age of N persons is x years. If M persons joins them, the average age is decreased by y years then the average age of new comers is x-(1+(N/M)) y years
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  • The average age of N persons is x years. If M persons left, then the average age is increased by y years, then the average age ofoutgoing persons is x+(1-(N/M))  y years.
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  • The average age of N persons is x years. If M persons left, then the average age is decreased by y years. Then the average age of outgoing persons is x-(1-(N/M)) y years
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  • In a group of N persons whose average age is increased by y years when a person of x years is replaced by a new man. Then the age of new comer is x + Ny years.
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  • The average temperature of Sunday, Monday, Tuesday and Wednesday was Xo C. The average temperature for Monday, Tuesday, Wednesday and Thursday was Yo C. If the temperature on Thursday is ao C then the temperature on Sunday (bo C) can be given as bo C = No of days (X -Y) + a 
    Here No. of days = 4.
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