Find Mean, Median, Mode & Range : Tricks & Formula

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Mean, Median, Mode, Range (With Formula) : গড়, মধ্যক, প্ৰচুৰক, বিস্তাৰ (সূত্ৰসহ)

1. Mean (Average): Mean is the average of a set of numbers. It is calculated by adding all the values and dividing by the total number of values.

Formula: Mean = Sum of observations / Number of observations ​

Mean = Sum of observations / Number of observations ​

Mean বা গড় হৈছে কিছুমান সংখ্যাৰ গড় মান। সকলো মান যোগ কৰি মুঠ সংখ্যাৰে ভাগ কৰিলে Mean পোৱা যায়।

2. Median (Middle Value) : Median is the middle value of a data set when numbers are arranged in ascending or descending order. If the number of observations is even, the median is the average of the two middle values.

Median হৈছে ঊৰ্ধ্বক্রম বা অৱৰোহ ক্রমত সাজি লোৱা তথ্যৰ মাজৰ মান। যদি সংখ্যাবোৰ জোৰ হয়, তেন্তে দুটা মাজৰ মানৰ গড় লোৱা হয়।

Formula: Median = Middle value of arranged data 

3. Mode (Most Frequent Value) : Mode is the value that appears most frequently in a data set. Mode হৈছে তথ্যসমূহত সৰ্বাধিক বাৰ দেখা দিয়া সংখ্যা।

Formula: Mode = Most frequent value 

4. Range (Difference): Range is the difference between the highest value and the lowest value in a data set. Range হৈছে তথ্যসমূহৰ সৰ্বোচ্চ মান আৰু সৰ্বনিম্ন মানৰ পাৰ্থক্য।

Formula: Range = Maximum value − Minimum value

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

1^st: Odd number of terms

Median = Middle value

Arrange in ascending order first

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

2^nd : 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 : গড় মান = 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 : মধ্য মান = 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 :মধ্য মান = 5

Mode

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

Solⁿ

4 appears most frequently

Mode = 4 : Mode = 4 (সৰ্বাধিক দেখা যায়)

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 → মুঠ ÷ সংখ্যা


• Median → Middle value : Median → মাজৰ মান


• Mode → Most frequent : Mode → সৰ্বাধিক দেখা মান