Statistics-Mean,Mode and Median - Future Study Point

Statistics-Mean,Mode and Median

mean,mode and median


Mean, mode and median are the terms of statistics which represent the central tendency of a data, The single value of the mean, mode or median tells us about the state of data. All of these three are important in solving statistical problems in economics, science, commerce, and other fields.

mean,mode and median


Mean- The mean of data represents the most common value of the data, it is calculated as follows.

When data is given as an individual series- Indidual series means when each value of the variable is given without showing its frequency.

Click for online shopping

Future Study Point.Deal: Cloths, Laptops, Computers, Mobiles, Shoes etc


Find out the average weight of 5 people whose weights are given as follows.

45 kg, 50 kg, 40 kg,60 kg and 55 kg


So, the most common weight or average weight of 5 people in the given data is 50

Disadvantages of mean– The mean is unable to represent the data in the condition when data is skewed (much differences between larger values and the rest of the individual values of the data), then the median would be truer to represent the data, see the following example.

maths marks of 5 friends in a test560951065


Median- Median is called the middle term of the data provided data should be ascending order, the mean of the above data is 47 which is not representing the data properly so here median of the data will the best to show the nature of data of maths marks of 5 friends in a test.

maths marks of 5 friends in a test510606595

n = 5 (odd number)

m = 60

The median of this data is 60 is representing the given data in a better way because of the difference between the largest value and median is lesser than the difference between the largest value and mean.

When the individual data is given and the number of observations are even

Direct Method for evaluating the Mean

Discreet series- When frequencies are also given with the values of variable then such a series is known as discreet series, see the example



Mean of  such a data is given as follows



∑f= 28




Determining the Median in case of discreet series-





Therefore the median of the above data is 55.

The other ways of calculating mean are following

 Assumed mean method for evaluating the Mean

  Assuming an observation as a mean(A) and then forming the third column and then writing the deviation(d) each observation about the mean that is equal to the difference between observation and the assumed mean keeping in view the sign convention of the numbers, thereafter forming 4 th column and evaluating fd the product of deviation and their corresponding frequencies. After the table is formed then calculate the value of mean from the following formula.

∑fd is the addition of the product of deviation and corresponding frequencies and ∑f is the sum of total frequencies of individual observations.

Click for online shopping

Future Study Point.Deal: Cloths, Laptops, Computers, Mobiles, Shoes etc

Step deviation method for evaluating Mean

 In this method, one more column is added d’ as compared to the assumed mean method, in this method deviation(d) is reduced by dividing the common factor(h )of all the deviations.

After evaluating d’ one more column of fd’ is also incorporated in the table and then calculate the mean from the following formula.

When the continuous series is given-

Class interval10-2020-3030-4040-5050-60



Sr.n0Class intervalf(Frequency)x(Classmark)fx




Other methods- (i) Assumed mean method- Already discussed above

 Step deviation method– Already discussed above

Median of the data when continuous series is given-

Class interval10-2020-3030-4040-5050-60


Solution- Median is calculated by using the following formula when continuous series is given

Class intervalFrequency(f)Cumulative frequency(cf)

The median group is N/2 th term of the series i.e N/2=40/2 = 20 th term which lies in 35 th term so the median group is 30-40


L = 30 (Lower limit of median class)

f =20 (Frequency of median class)

Hence the median of the given series is 32.5

The mode – In a series, the term with the highest frequency is known as mode of the series.

Mode of an individual series- When the individual measurements of the variable are given without showing their frequency then the terms with high frequency is known as a mode of the series.


Example- The performances of a student in 5 tests are given as follows, find the mode of data.


40 has the highest frequency so the mode of the above data is 40

Mode in a discreet series- When the frequency is also given of each term then such a series is known as discreet series.

Age of students in a class(in years)1315161412
Number of students764158

In the given data most numbers of students are of the age 14 so the mode of the data is 14.

Mode of the continuous series- Find the mode of the following series

The age of employs(in years)20-3030-4040-5050-6060-70
The number of employs305025152


Study notes of Maths & Science

Solution –

The ages of employs(in years)frequency(f)


The mode(M ) of continuous series is calculated as follows

The class 30-40 has the highest frequency so it is mode group of above data

L = 40(lower limit of mode group)

f0= 30(preceding frequency of mode group)

f1= 50( frequency of mode group)

f2= 25 (successor   frequency of mode group)

i= Class interval of mode group



M = 30+ 4.44

M = 34.44

Hence the mode of the series is 34.44 

The relationship between Mean,Mode and Median

Mode = 3×Median – 2×Mean

NCERT Solutions of Science and Maths for Class 9,10,11 and 12

NCERT Solutions for class 9 maths

Chapter 1- Number SystemChapter 9-Areas of parallelogram and triangles
Chapter 2-PolynomialChapter 10-Circles
Chapter 3- Coordinate GeometryChapter 11-Construction
Chapter 4- Linear equations in two variablesChapter 12-Heron’s Formula
Chapter 5- Introduction to Euclid’s GeometryChapter 13-Surface Areas and Volumes
Chapter 6-Lines and AnglesChapter 14-Statistics
Chapter 7-TrianglesChapter 15-Probability
Chapter 8- Quadrilateral

NCERT Solutions for class 9 science 

Chapter 1-Matter in our surroundingsChapter 9- Force and laws of motion
Chapter 2-Is matter around us pure?Chapter 10- Gravitation
Chapter3- Atoms and MoleculesChapter 11- Work and Energy
Chapter 4-Structure of the AtomChapter 12- Sound
Chapter 5-Fundamental unit of lifeChapter 13-Why do we fall ill ?
Chapter 6- TissuesChapter 14- Natural Resources
Chapter 7- Diversity in living organismChapter 15-Improvement in food resources
Chapter 8- MotionLast years question papers & sample papers

NCERT Solutions for class 10 maths

Chapter 1-Real numberChapter 9-Some application of Trigonometry
Chapter 2-PolynomialChapter 10-Circles
Chapter 3-Linear equationsChapter 11- Construction
Chapter 4- Quadratic equationsChapter 12-Area related to circle
Chapter 5-Arithmetic ProgressionChapter 13-Surface areas and Volume
Chapter 6-TriangleChapter 14-Statistics
Chapter 7- Co-ordinate geometryChapter 15-Probability
Chapter 8-Trigonometry

CBSE Class 10-Question paper of maths 2021 with solutions

CBSE Class 10-Half yearly question paper of maths 2020 with solutions

CBSE Class 10 -Question paper of maths 2020 with solutions

CBSE Class 10-Question paper of maths 2019 with solutions

NCERT Solutions for Class 10 Science

Chapter 1- Chemical reactions and equationsChapter 9- Heredity and Evolution
Chapter 2- Acid, Base and SaltChapter 10- Light reflection and refraction
Chapter 3- Metals and Non-MetalsChapter 11- Human eye and colorful world
Chapter 4- Carbon and its CompoundsChapter 12- Electricity
Chapter 5-Periodic classification of elementsChapter 13-Magnetic effect of electric current
Chapter 6- Life ProcessChapter 14-Sources of Energy
Chapter 7-Control and CoordinationChapter 15-Environment
Chapter 8- How do organisms reproduce?Chapter 16-Management of Natural Resources

NCERT Solutions for class 11 maths

Chapter 1-SetsChapter 9-Sequences and Series
Chapter 2- Relations and functionsChapter 10- Straight Lines
Chapter 3- TrigonometryChapter 11-Conic Sections
Chapter 4-Principle of mathematical inductionChapter 12-Introduction to three Dimensional Geometry
Chapter 5-Complex numbersChapter 13- Limits and Derivatives
Chapter 6- Linear InequalitiesChapter 14-Mathematical Reasoning
Chapter 7- Permutations and CombinationsChapter 15- Statistics
Chapter 8- Binomial Theorem Chapter 16- Probability

CBSE Class 11-Question paper of maths 2015

CBSE Class 11 – Second unit test of maths 2021 with solutions

NCERT Solutions for Class 11 Physics

Chapter 1- Physical World

chapter 3-Motion in a Straight Line

NCERT Solutions for Class 11 Chemistry

Chapter 1-Some basic concepts of chemistry

Chapter 2- Structure of Atom

NCERT Solutions for Class 11 Biology

Chapter 1 -Living World

NCERT solutions for class 12 maths

Chapter 1-Relations and FunctionsChapter 9-Differential Equations
Chapter 2-Inverse Trigonometric FunctionsChapter 10-Vector Algebra
Chapter 3-MatricesChapter 11 – Three Dimensional Geometry
Chapter 4-DeterminantsChapter 12-Linear Programming
Chapter 5- Continuity and DifferentiabilityChapter 13-Probability
Chapter 6- Application of DerivationCBSE Class 12- Question paper of maths 2021 with solutions
Chapter 7- Integrals
Chapter 8-Application of Integrals

Class 12 Solutions of Maths Latest Sample Paper Published by CBSE for 2021-22 Term 2

Class 12 Maths Important Questions-Application of Integrals

Class 12 Maths Important questions on Chapter 7 Integral with Solutions for term 2 CBSE Board 2021-22

Solutions of Class 12 Maths Question Paper of Preboard -2 Exam Term-2 CBSE Board 2021-22

Solutions of class 12  maths question paper 2021 preboard exam CBSE Solution











Scroll to Top