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 =
- Weighted Average =
- Arithmetic Mean = (a
_{1}+ a_{2}+ a_{3}â€¦.a_{n}) / n - Geometric Mean =
- Harmonic Mean =

__For two numbers a and b:__â‡’ AM = (a + b)/2

EduRev's Tip:AM â‰¥ GM â‰¥ HM is always true. They will be equal if all elements are equal to each other. If I have just two values then GM^{2}= AM*HM

EduRev's Tip:The sum of deviation (D) of each element with respect to the average is 0.

â‡’ D = (x_{1}- x_{avg}) + (x_{2}- x_{avg}) + (x_{3}- x_{avg}) ... + (x_{1}- x_{avg}) = 0

EduRev's Tip:x_{avg}= (x_{assumed}_{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 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 â€“ (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 â€“ The average will be the middle term.
- When number of terms is even â€“ 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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