Examcrazy Logo
Search Colleges PSU exams 2011 Preparation Engineering books How to Prepare for Exams Technical Freshers Jobs
Freshers technical Jobs at ExamCrazy.Com
Click to see all available jobs now!!
Share |
  Follow us|  twitter  Orkut  facebook
Maths Formula Tips
   Quadratic Equations and Expressions Formula & Tips
   Complex Number Formula & Tips
   Permutation and Combination Formulas
   Probability Formula & Tips
   Progression and Series Formula & Tips
   Binomial Theorem Formula & Tips
   Trigonometric Ratio and Identities
   Trigonometric Equations Formula & Tips
   Inverse Trigonometric Functions
   Properties & Solution of Triangle
   Height and Distance Formula & Tips
   Co-ordinate Geometry Point Formulas & Tips
   Co-ordinate Geometry Straight Line
   Co-ordinate Geometry circle
   Co-ordinate Geometry Parabola
   Co-ordinate Geometry Ellipse
   Co-ordinate Geometry Hyperbola
   Measures of central tendency & dispersion
   Matrices & Determinants
   Function Formula & Tips
   Calculus Limit Formula & Tips
   Calculus Differentiation
   Calculus Application of Derivatives
   Calculus Indefinite Integration
   Calculus Definite Integration
   Calculus Differential Equations
   Vectors Formula & Tips
   Three Dimensional Geometry
Other Maths Tutorials
   Introduction to Vectors and 3-D Geometry
   Matrices and Determinant Tutorials
   Differential Equation Tutorials
   Maths Tutorials for AIEEE IIT Pre Engineering
   Physics Tutorials for AIEEE IIT Pre Engineering
   Chemistry Tutorials for AIEEE IIT Pre Engineering
More Engineering Links
   Directory of coaching Institutes
   Govt engg college rankings
   Private engg college rankings
   Admission notifications for Mtech/PhD
   All Engineering Colleges in India
Measures Of Central Tendency And Dispersion

1 Arithmetic mean:
(i) For ungrouped data (individual series) ` x =

(ii) For grouped data (continuous series)
(a) Direct method `x = where xi , I = 1 .. n be n observations and fi be their corresponding frequencies
(b) short cut method : `x = A + åfidi / åfi) where A = assumed mean, di = xi - A = deviation for each term
2 Properties of A.M.
(i) In a statistical data the sum of the deviation of items form A.M. is alwalys zero.
(ii) If each of the n given observation be doubled, then their mean is doubled
(iii) If `x is the mean of x1, x2, , xn . the mean of ax1, x2, .. , axn is a `x where a is any number different form zero
(iv) Arithmetic mean is independent of origin i.e. it is x effected by any change in origin.
3 Geometric mean:
(i) For ungrouped data G.M. = (x1 x2 x3 .. xn)1/n or
G.M. = antilog
(ii) For grouped data G.M. = (xf11 xf22 .. xfnn)1/N , where N = i=1 ån fi

4 Harmonic mean Harmonic mean is reciprocal of arithmetic mean of reciprocals.
(i) For ungrouped data H.M. =
(ii) For grouped data H.M. =
5 Relation between A.M., G.M and H.M.
A.M. ³ G.M. ³ H.M.
Equation holds only when all the observations in the series are same
6 Msdian:
(a) Individual series (ungrouped data) : If data is raw, arrange in ascending or descending order and n be the no. of observations . If n is odd, Median = value of ((n+1) / 2))th observation If n is even, median = (1/2) [value of (n/2)th + value of ((n/2) + 1)th] observation.
(b) Discrete series: First find cumulative frequencies of the variables arranged in ascending or descending order and Mediain = {(n+1) / 2}th observation, where n is cumulative frequency.
(c) Continuous distribution (grouped data)
(i) For series in ascending order
Median = e +
e = Lower limit of the median class.
f = Frequency of the median class.
N = Sum of the all frequencies.
i = The width of the median class.
C = Cumulative frequency of the class preceding to median class.
(ii) For series in descending order Median = u -
Where u = upper limit of median class.
7 Mode:
(i) For individual series: In the case of individual series, the value which is repeated maximum number of times is the mode of the series.
(ii) For discrete frequency distribution series: In the case of discrete frequency distribution, mode is the value of the variate corresponding to the maximum frequency.
(iii) For continuous frequency distribution : first find the model class i.e. the class which has maximum frequency for continuous series

e1 = Lower limit of the model class.
f1 = Frequency of the model class.
f0 = Frequency of the class preceding mode class.
f2 = Frequency of the class succeeding model class.
i= Size of the model class.
8 Relation between mean, mode & median:
(i) In symmetrical distribution : mean = mode = median
(ii) In Moderately symmetrical distribution : mode = 3 median 2 mean

Measure of Dispersion:
The degree to which numerical data tend to spread about an average value is called variation or dispersion popular methods of measure of dispersion.
(a) Individual series (ungrouped data)
1 Mean deviationMean deviation = (å|x-S| / n)
Where n = number of terms, S = deviation of variety form mean mode , median
(b) Continuous series (grouped data)

Mean deviation is the least when measured from the median.
2 Standerd Deviation :
S.D. (s) is the squere root of the arithmetic mean of the squares of the deviations of the terms from their A.M.
(a) for individual series (ungrouped data)
where `x = Arithmetic mean of the series N = Total frequency
(b) For continuous series (grouped data)
(i) Direct method s =
`x = Arithmetic mean of series
X1 = mid value of the class
f1 = Frequency of the corresponding x1
N = åf = Total frequency
(ii) Short cut method

d = x - A = Derivation from assumed mean A
f = Frequency of item (term)
N = åf = Total frequency.
Variance Square of standard direction
i.e. variance = (S.D.)2 = (s)2
Coefficient of variance = Coefficient of S.D. x 100 = (s / x) x 100

Discuss About Measures Of Central Tendency And Dispersion
Measures of Central Tendency and Dispersion Formulas and Cheat Sheets
Discussion forum for Measures of Central Tendency and Dispersion Formulas and Cheat Sheets Formulas and Cheat Sheets
Thread / Thread Starter Last Post Replies Views

To start your new thread you must login here.
New user signup at ExamCrazy.com Exam Crazy
To reply/post a comment you need to login, Use your user name and password to login if you are already registered else register here

(Members Login)

  About us | Privacy Policy | Terms and Conditions | Contact us | Email: support@Examcrazy.com  
Copyright 2009 Extreme Testing House, India. All rights reserved.