Important Formula and Tips: Averages Quant Notes | EduRev

UPSC CSAT: Quantitative Aptitude (Quant)

CAT : Important Formula and Tips: Averages Quant Notes | EduRev

The document Important Formula and Tips: Averages Quant Notes | EduRev is a part of the CAT Course UPSC CSAT: Quantitative Aptitude (Quant).
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Basic Formulae

  • Simple Average = Important Formula and Tips: Averages Quant Notes | EduRev
  • Weighted Average = Important Formula and Tips: Averages Quant Notes | EduRev
  • Arithmetic Mean = (a1 + a2 + a3 ….an) / n
  • Geometric Mean = Important Formula and Tips: Averages Quant Notes | EduRev
  • Harmonic Mean = Important Formula and Tips: Averages Quant Notes | EduRev

For two numbers a and b:
⇒ AM = (a + b)/2
Important Formula and Tips: Averages Quant Notes | EduRev


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))


Median and Mode

  • Median of a finite list of numbers can be found by arranging all the observations from lowest value to highest value and picking the middle one.
  • The mode is the value that occurs most often:
    Mode = 3*Median - 2*Mean
    Important Formula and Tips: Averages Quant Notes | EduRev


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 

  • Age of new person= Age of person who left + (Increase in average * total number of persons)

(b) If the average is decreased, then

  • Age of new person= Age of person who left – (Decrease in average * total number of persons)

2. When a person joins the group

(a) In case of an increase in average

  • Age of new member = Previous average+ (Increase in average * Number of members including new member)

(b) In case of a decrease in average

  • Age of new member = Previous average - (Decrease in average * Number of members including new member)

In the Arithmetic Progression, there are two cases:

  • When the number of terms is odd – The average will be the middle term.
  • When number of terms is even – The average will be the average of two middle terms.

Note:

Sum of 1st n consecutive natural numbers = [n(n+1)]/2

Average of 1st n consecutive natural numbers = (n+1)/2

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