Tricks to find Mean, Median, Mode

Tricks to find Mean, Median, Mode


1. Mean (Average) Trick


Formula


Mean = Sum of all observations / Number of observations


Quick Trick


·   Add fast using pair method
Ex: 12, 18, 20, 10
Pair them: (12+18) = 30, (20+10) = 30


Mean = 30+30 / 4 = 60 / 4 = 15


2. Median Trick


1st: Odd number of terms


Median = Middle value


Arrange in ascending order first


Ex: 5, 2, 9 → Arrange: 2, 5, 9 → Median = 5


2nd : Even number of terms


Median = Middle 2 values/2


Ex: 4, 8, 6, 2 → Arrange: 2, 4, 6, 8→ Median = 4+6/2 = 5


3. Mode Trick


Mode = Number that appears the most


Ex: 3, 7, 3, 2, 9, 3
Mode = 3 (repeat most)


If two repeat same times → Bimodal


Ex: 4, 6, 4, 8, 8
Mode = 4 & 8 (both repeat)


Special Quick Tips - By Points



  • Mean → Pair numbers to add quickly

  • Median → Always arrange in ascending order first

  • Mode → Find the number that repeats the most

  • If no number repeats → Mode = No mode

  • If 2 numbers repeat equally → Bimodal

  • If 3 numbers repeat equally → Trimodal


Super Quick Revision



  • Mean → total ÷ count

  • Median → middle (after arranging)

  • Mode → most repeated


Q. A dataset consists of x, 2x, 3x, and 4x. If the mean is 12.5, what is the median 


Soln


Given:


Dataset: x, 2x, 3x, 4x
Mean = 12.5


Use mean to find x


Mean = x+2x+3x+4x / 4 =10x/4 = 2.5x


              2.5x = 12.5


                   x = 12.5/2.5 = 5


Substitute values in the dataset X = 5


So the dataset becomes: 5,10,15,20


Find the Median


Since there are 4 numbers (even count):


Median = 2nd value+3rd value/2 =10+15/2 = 25/2 =12.5


Ans:12.5


Mean (Average)


Q. Find the mean of 10, 20, 30, 40


Soln


Sum = 10 + 20 + 30 + 40 = 100
Number of values = 4


Mean = 100 ÷ 4 = 25


Mean = 25 : āĻ—āĻĄāĻŧ āĻŽāĻžāĻ¨ = 25


Median (Odd case)


Q. Find the median of 7, 3, 9, 1, 5


Soln


Arrange: 1, 3, 5, 7, 9
Middle value = 5


Median = 5 : āĻŽāĻ§ā§āĻ¯ āĻŽāĻžāĻ¨ = 5


Median (Even case)


Q. Find the median of 4, 2, 8, 6


Soln


Arrange: 2, 4, 6, 8
Median = (4 + 6) ÷ 2 = 5


Median = 5 :āĻŽāĻ§ā§āĻ¯ āĻŽāĻžāĻ¨ = 5


Mode


Q. Find the mode of 2, 4, 4, 5, 6, 4, 7


Soln


4 appears most frequently


Mode = 4 : Mode = 4 (āĻ¸ā§°ā§āĻŦāĻžāĻ§āĻŋāĻ• āĻĻā§‡āĻ–āĻž āĻ¯āĻžāĻ¯āĻŧ)


Mixed (Mean + Median + Mode)


Q. Find mean, median, and mode of 3, 6, 9, 6, 12


Soln


Arrange: 3, 6, 6, 9, 12


Mean : Sum = 36, Mean = 36 ÷ 5 = 7.2, Mean = 7.2


Median : Middle value = 6. Median = 6


Mode : 6 repeats most, Mode = 6


Notes



  • Mean → Sum ÷ Number : Mean → āĻŽā§āĻ  ÷ āĻ¸āĻ‚āĻ–ā§āĻ¯āĻž

  • Median → Middle value : Median → āĻŽāĻžāĻœā§° āĻŽāĻžāĻ¨

  • Mode → Most frequent : Mode → āĻ¸ā§°ā§āĻŦāĻžāĻ§āĻŋāĻ• āĻĻā§‡āĻ–āĻž āĻŽāĻžāĻ¨