SlideShare a Scribd company logo
STATISTICS
   INDIVIDUAL        DISCRET         CONTINUOUS
    S.no Marks   Marks    Freq.   Marks    Freq.

    1    30      20       8       10 -20   8

    2    40      30       12      20 -30   12

    3    50      40       20      30 -40   20

    4    60      50       10      40 -50   10

    5    70      60       6       50 -60   6
marks   Freq.(f)   Cumm.freq.(cf)

20      8          8


30      12         20


40      20         40


50      10         50


60      6          56
 Measuresof Central Tendency are used to
             describe the set of data.

                     Mean
                    Median
                     Mode




1.Arithmetic Mean

2.Shortcut Method to Mean

3.Direct Method to mean

4.Shortcut Method for Direct Method

5.Calculation of Mean:-

             *Individual series
             *Discret series
             *continuous series
Mean
The mean is also known as the average of the set.
 Add all of the number is in the set and divide this
 sum by the number of items in the set.
1.Easy to understand.
2.Simple to compute.
3. Based on all items.
4.Affected by extreme observation.
5.Capable of further calculation.
1.Arithmetic Mean:

                          X
              X
                       N
     X      X1 X 2 X 3 ..... Xn
  N =No. of observations/items in a series
                  x
                  20

                  30

                  10
 2.   Shortcut method to Mean   Ex:-
                                 X      d= X-A
                          d
            X     A              20
                          N
                Assumed mean     30
           A
            d    X    A          40


                                 50
 3.Direct   Method:-   Marks(X)   f   fx

               f x      20         4
   X
                  f     30         2

                        40         3
       f      N
                        50         1
 4.Shortcut     Method for Direct Method:-
                                f d
            X      A
                                 f
           d      x       A
 Marks f        d = x-A   f.d

 20    8

 30    12

 40    20

 50    10
 Calculation      of Mean in Continuous series:-
                          f ( m)
              X
                            f
              m     mid point of class interval
  Marks (x)   f       m         f (m)
  10 – 20     8
  20 – 30     12
  30 – 40     20
  40 – 50     10
  50 - 60     6
   Since its definition is precise and clear,
    calculation is easy and its value always
    determinate.

   Its chief merit consists in the fact that it take
    onto consideration every item in the data.

   NO special arrangement of data is necessary
    while calculating it, unlike median and mode
    where we have to arrange and group the data in
    a certain manner.

   It forms a good basis of comparison while
    comparing different groups of numerical data.
   Omission of even a single item of the data gives an
    incorrect value of the A.M., unlike median and mode
    where extreme items can simply be discarded.

   It may not identical with any one of the items of the
    data. That is, it may not be one of the figures that
    comprise the data.

   The fact that it gives a large weight to extreme items
    is its handicap since it then fails to be a good
    representatives. That is, the value of A.M. of the
    data consisting of very and very small items may lead
    to wrong conclusions.

   It cannot be used in qualitative studies, unlike the
    median.
1.Definition
2.Characteristics
3.Calculating median:-
            *Individual series
            *Discret series
            *Continuous series
4.Advantages & Disadvantages of
median.
 The   value of the middle item of a series
    that is ordered either in the ascending or
    descending order of magnitude is called
    the median.
1.Measure of central tendency     marks   order   marks   order
2.Middle value in ordered
      sequence                    40              30
      If n is odd, middle                        60
       value of sequence          20
                                                  10
      If n is even, average of   50
       2 middle values. (n= no                    40
       of items in a series)      10              20
                                  30              50
 Odd   series:- middle value of sequence.(series
    must be in order)

 Even   series:-
            median=
                       N 1
                          th item
                        2
                     N No. of observation
   Arrange the data in ascending or descending order
   Find c.f.
   Apply     N 1
                      th
                2
   Look for the value in cf. corresponding figure to cf is the median.

     Income No. of               cf
            person(f)

     800         16
     1000        24
     1500        26
     1800        30
     2000        20
     2500        6
   Method:- same as discrete series but instead of         N 1
                                                             2
      N
apply 2   to determine the median class.
Then apply,
                      N
                                cf
Median = L            2               *i
                            f
           L= lower limit of the median class
           cf= cf of the class preciding the median class
            f= frequency of median class
            i=class interval
Marks     No.of      cf
          student(f)
0–5       4                   N
                              2
5 – 10    5
                                  N
10- 15    10                              cf
                          L       2            *i
                                      f
15 – 20   10
   Most of the conditions of an ideal average are
    satisfied by it.

   The median is of immense use while estimating
    qualities such as honestly, intelligence, virtue,
    morality etc. and proves to be a good
    representative.

   It’s possible to find the median by knowing only
    the values of central items and the no. of items.
    That is, the values of extreme items are not
    necessary for finding the median.
   An irregular series is characterized by extreme
    variations between the items, in the case of such
    a series the median fails to be representative.

   Arrangement of the data either in the ascending
    order of the magnitude or descending order is
    the chief requisite. This process is tedious when
    the data is vast.

   Sometimes the medians may exist between two
    values, thus involving the work of estimation.

   Unlike the A.M., it is not possible to find the
    total value of all items if we know the value of
    the median and the no. of items.
 QUARTILE:- It divides the entire series into
                   4 equal parts.
Quartiles in:-
                 # Individual & discrete series
                 # Continuous series
N       1
          Q1                       th
                           4
                        N          1
          Q3       3                   th
                               4



       N                                    N
Q1       th                            Q3 3   th
       4                                    4
          N                                       N
                  cf                            3         cf
          4                                       4
Q1 L                   *i              Q3   L                  *i
              f                                       f
Find Q1 & Q3


 class     f    cf

 0-5       7

 5 – 10    18

 10 -15    25

 15 – 20   30

 20 – 25   20
The value of the item in a
variable that is repeated the
greatest number of times is
called the mode.
The number that repeats the
most
   3, 4, 4, 10, 15, 16, 18
             4 is the
              mode
there may be more than one mode

3, 3, 4, 4, 4, 7, 9, 9, 9

         4 & 9 are the modes
when there is only single value(f) which is highest.

                f1 f 
       M L              i
            2 f1 f  f 2

L= lower limit of model class
f1= frequency of model class
fo= frequency of class preciding the model class
f2= frequency of class successiding the model class
Calculate mode


                             f1 f 
marks     No. of    M L              i
          student        2 f1 f  f 2
0 – 10    10

10 – 20   12

20 – 30   15

30 – 40   8

40 - 50   5
When     there    are    two     similar
frequencies/values which are highest.


MODE = 3 MEDIAN – 2MEAN
1.It is the most predominant item in a
discrete series.



2.If a continuous series is a regular one i.e.
with the maximum frequency in the centre
the mode can be calculated easily without
knowing the frequencies at the two
extremities of the series.

3.It is very useful average in studying business
relating to sales, profits etc.
1.It is quite possible that in certain types of
data it may not be properly defined & hence it
may be indeterminate & indefinite.

2.The value of the mode is not the value
obtained by considering the value of every item
of the data.

3.In the case of an irregular series it is not very
easy to determine the mode.

4.It is quite possible that in certain instances
there may be two or more values for the mode.
BOOK:- Quantitative Techniques in
Business by : Dr. Aditham B.Rao

More Related Content

What's hot

Mean, Median, Mode: Measures of Central Tendency
Mean, Median, Mode: Measures of Central Tendency Mean, Median, Mode: Measures of Central Tendency
Mean, Median, Mode: Measures of Central Tendency Jan Nah
 
Measures of central tendency
Measures of central tendencyMeasures of central tendency
Measures of central tendencyRaj Teotia
 
Math 7 lesson 11 properties of real numbers
Math 7   lesson 11 properties of real numbersMath 7   lesson 11 properties of real numbers
Math 7 lesson 11 properties of real numbersAriel Gilbuena
 
Lesson 2 percentiles
Lesson 2   percentilesLesson 2   percentiles
Lesson 2 percentileskarisashley
 
Mean, median, and mode
Mean, median, and modeMean, median, and mode
Mean, median, and modeguest455435
 
Mean, median, mode, & range ppt
Mean, median, mode, & range pptMean, median, mode, & range ppt
Mean, median, mode, & range pptmashal2013
 
Measures of Central Tendency
Measures of Central TendencyMeasures of Central Tendency
Measures of Central TendencySuresh Babu
 
Chapter 2: Frequency Distribution and Graphs
Chapter 2: Frequency Distribution and GraphsChapter 2: Frequency Distribution and Graphs
Chapter 2: Frequency Distribution and GraphsMong Mara
 
Statistics (Mean, Median, Mode)
Statistics (Mean, Median, Mode)Statistics (Mean, Median, Mode)
Statistics (Mean, Median, Mode)Sherzad Daudzai
 
Measures of dispersion
Measures of dispersionMeasures of dispersion
Measures of dispersionJagdish Powar
 
What is a spearmans rank order correlation?
What is a spearmans rank order correlation?What is a spearmans rank order correlation?
What is a spearmans rank order correlation?Ken Plummer
 
Estimation & Approximation
Estimation & ApproximationEstimation & Approximation
Estimation & ApproximationSteve Bishop
 
Measure OF Central Tendency
Measure OF Central TendencyMeasure OF Central Tendency
Measure OF Central TendencyIqrabutt038
 

What's hot (20)

Frequency Distributions
Frequency DistributionsFrequency Distributions
Frequency Distributions
 
Histogram
HistogramHistogram
Histogram
 
Mean, Median, Mode: Measures of Central Tendency
Mean, Median, Mode: Measures of Central Tendency Mean, Median, Mode: Measures of Central Tendency
Mean, Median, Mode: Measures of Central Tendency
 
Mode
ModeMode
Mode
 
Pictograms
PictogramsPictograms
Pictograms
 
Median & mode
Median & modeMedian & mode
Median & mode
 
Measures of central tendency
Measures of central tendencyMeasures of central tendency
Measures of central tendency
 
Math 7 lesson 11 properties of real numbers
Math 7   lesson 11 properties of real numbersMath 7   lesson 11 properties of real numbers
Math 7 lesson 11 properties of real numbers
 
Lesson 2 percentiles
Lesson 2   percentilesLesson 2   percentiles
Lesson 2 percentiles
 
F test
F testF test
F test
 
Mean, median, and mode
Mean, median, and modeMean, median, and mode
Mean, median, and mode
 
Mean, median, mode, & range ppt
Mean, median, mode, & range pptMean, median, mode, & range ppt
Mean, median, mode, & range ppt
 
Measures of Central Tendency
Measures of Central TendencyMeasures of Central Tendency
Measures of Central Tendency
 
Chapter 2: Frequency Distribution and Graphs
Chapter 2: Frequency Distribution and GraphsChapter 2: Frequency Distribution and Graphs
Chapter 2: Frequency Distribution and Graphs
 
Statistics (Mean, Median, Mode)
Statistics (Mean, Median, Mode)Statistics (Mean, Median, Mode)
Statistics (Mean, Median, Mode)
 
Measures of dispersion
Measures of dispersionMeasures of dispersion
Measures of dispersion
 
What is a spearmans rank order correlation?
What is a spearmans rank order correlation?What is a spearmans rank order correlation?
What is a spearmans rank order correlation?
 
Estimation & Approximation
Estimation & ApproximationEstimation & Approximation
Estimation & Approximation
 
Operations on Real Numbers
Operations on Real NumbersOperations on Real Numbers
Operations on Real Numbers
 
Measure OF Central Tendency
Measure OF Central TendencyMeasure OF Central Tendency
Measure OF Central Tendency
 

Viewers also liked

3.1 measures of central tendency
3.1 measures of central tendency3.1 measures of central tendency
3.1 measures of central tendencyleblance
 
Data Structure: TREES
Data Structure: TREESData Structure: TREES
Data Structure: TREESTABISH HAMID
 
Stattistic ii - mode, median, mean
Stattistic ii - mode, median, meanStattistic ii - mode, median, mean
Stattistic ii - mode, median, meanamsy1224
 
Calculating the mean, median and mode
Calculating the mean, median and modeCalculating the mean, median and mode
Calculating the mean, median and modecarltimmis
 
Measure of central tendency (Mean, Median and Mode)
Measure of central tendency (Mean, Median and Mode)Measure of central tendency (Mean, Median and Mode)
Measure of central tendency (Mean, Median and Mode)Shakehand with Life
 
3.3 Mean, Median, Mode, Formulas
3.3 Mean, Median, Mode, Formulas3.3 Mean, Median, Mode, Formulas
3.3 Mean, Median, Mode, FormulasJessca Lundin
 
Mean Median Mode
Mean Median ModeMean Median Mode
Mean Median Modehiratufail
 
Measures of central tendency
Measures of central tendencyMeasures of central tendency
Measures of central tendencyChie Pegollo
 

Viewers also liked (9)

3.1 measures of central tendency
3.1 measures of central tendency3.1 measures of central tendency
3.1 measures of central tendency
 
Data Structure: TREES
Data Structure: TREESData Structure: TREES
Data Structure: TREES
 
Stattistic ii - mode, median, mean
Stattistic ii - mode, median, meanStattistic ii - mode, median, mean
Stattistic ii - mode, median, mean
 
Calculating the mean, median and mode
Calculating the mean, median and modeCalculating the mean, median and mode
Calculating the mean, median and mode
 
Measure of Central Tendency
Measure of Central TendencyMeasure of Central Tendency
Measure of Central Tendency
 
Measure of central tendency (Mean, Median and Mode)
Measure of central tendency (Mean, Median and Mode)Measure of central tendency (Mean, Median and Mode)
Measure of central tendency (Mean, Median and Mode)
 
3.3 Mean, Median, Mode, Formulas
3.3 Mean, Median, Mode, Formulas3.3 Mean, Median, Mode, Formulas
3.3 Mean, Median, Mode, Formulas
 
Mean Median Mode
Mean Median ModeMean Median Mode
Mean Median Mode
 
Measures of central tendency
Measures of central tendencyMeasures of central tendency
Measures of central tendency
 

Similar to statistics

Similar to statistics (20)

Measures of Central Tendancy
Measures of Central TendancyMeasures of Central Tendancy
Measures of Central Tendancy
 
Central tendency
Central tendencyCentral tendency
Central tendency
 
Measures of central tendency
Measures of central tendencyMeasures of central tendency
Measures of central tendency
 
Median
MedianMedian
Median
 
Chapter 3
Chapter 3Chapter 3
Chapter 3
 
Arithmetic mean
Arithmetic meanArithmetic mean
Arithmetic mean
 
S1 pn
S1 pnS1 pn
S1 pn
 
Module stats
Module statsModule stats
Module stats
 
Module
ModuleModule
Module
 
mean median mode
 mean median mode mean median mode
mean median mode
 
test & measuement
test & measuementtest & measuement
test & measuement
 
ap_stat_1.3.ppt
ap_stat_1.3.pptap_stat_1.3.ppt
ap_stat_1.3.ppt
 
Median - Gropued and Ungrouped Data.pdf
Median - Gropued and Ungrouped Data.pdfMedian - Gropued and Ungrouped Data.pdf
Median - Gropued and Ungrouped Data.pdf
 
MEASURES OF CENTRAL TENDENCY
MEASURES OF CENTRAL TENDENCYMEASURES OF CENTRAL TENDENCY
MEASURES OF CENTRAL TENDENCY
 
Statistics
StatisticsStatistics
Statistics
 
Qt notes
Qt notesQt notes
Qt notes
 
MEDIAN.pptx
MEDIAN.pptxMEDIAN.pptx
MEDIAN.pptx
 
S5 pn
S5 pnS5 pn
S5 pn
 
statistics 10th (1) (3).pdf
statistics 10th (1) (3).pdfstatistics 10th (1) (3).pdf
statistics 10th (1) (3).pdf
 
Measure-of-central-tendency-median.statistics
Measure-of-central-tendency-median.statisticsMeasure-of-central-tendency-median.statistics
Measure-of-central-tendency-median.statistics
 

Recently uploaded

falcon-invoice-discounting-a-premier-platform-for-investors-in-india
falcon-invoice-discounting-a-premier-platform-for-investors-in-indiafalcon-invoice-discounting-a-premier-platform-for-investors-in-india
falcon-invoice-discounting-a-premier-platform-for-investors-in-indiaFalcon Invoice Discounting
 
State of D2C in India: A Logistics Update
State of D2C in India: A Logistics UpdateState of D2C in India: A Logistics Update
State of D2C in India: A Logistics UpdateRedSeer
 
Equinox Gold Corporate Deck May 24th 2024
Equinox Gold Corporate Deck May 24th 2024Equinox Gold Corporate Deck May 24th 2024
Equinox Gold Corporate Deck May 24th 2024Equinox Gold Corp.
 
Using Generative AI for Content Marketing
Using Generative AI for Content MarketingUsing Generative AI for Content Marketing
Using Generative AI for Content MarketingChuck Aikens
 
Byrd & Chen’s Canadian Tax Principles 2023-2024 Edition 1st edition Volumes I...
Byrd & Chen’s Canadian Tax Principles 2023-2024 Edition 1st edition Volumes I...Byrd & Chen’s Canadian Tax Principles 2023-2024 Edition 1st edition Volumes I...
Byrd & Chen’s Canadian Tax Principles 2023-2024 Edition 1st edition Volumes I...ssuserf63bd7
 
Evolution and Growth of Supply chain.pdf
Evolution and Growth of Supply chain.pdfEvolution and Growth of Supply chain.pdf
Evolution and Growth of Supply chain.pdfGutaMengesha1
 
India’s Recommended Women Surgeons to Watch in 2024.pdf
India’s Recommended Women Surgeons to Watch in 2024.pdfIndia’s Recommended Women Surgeons to Watch in 2024.pdf
India’s Recommended Women Surgeons to Watch in 2024.pdfCIOLOOKIndia
 
Easy Way to Download and Set Up Gen TDS Software on Your Computer
Easy Way to Download and Set Up Gen TDS Software on Your ComputerEasy Way to Download and Set Up Gen TDS Software on Your Computer
Easy Way to Download and Set Up Gen TDS Software on Your ComputerSAG Infotech
 
Special Purpose Vehicle (Purpose, Formation & examples)
Special Purpose Vehicle (Purpose, Formation & examples)Special Purpose Vehicle (Purpose, Formation & examples)
Special Purpose Vehicle (Purpose, Formation & examples)linciy03
 
What are the main advantages of using HR recruiter services.pdf
What are the main advantages of using HR recruiter services.pdfWhat are the main advantages of using HR recruiter services.pdf
What are the main advantages of using HR recruiter services.pdfHumanResourceDimensi1
 
Falcon Invoice Discounting Setup for Small Businesses
Falcon Invoice Discounting Setup for Small BusinessesFalcon Invoice Discounting Setup for Small Businesses
Falcon Invoice Discounting Setup for Small BusinessesFalcon investment
 
Business Valuation Principles for Entrepreneurs
Business Valuation Principles for EntrepreneursBusiness Valuation Principles for Entrepreneurs
Business Valuation Principles for EntrepreneursBen Wann
 
April 2024 Nostalgia Products Newsletter
April 2024 Nostalgia Products NewsletterApril 2024 Nostalgia Products Newsletter
April 2024 Nostalgia Products NewsletterNathanBaughman3
 
LinkedIn Masterclass Techweek 2024 v4.1.pptx
LinkedIn Masterclass Techweek 2024 v4.1.pptxLinkedIn Masterclass Techweek 2024 v4.1.pptx
LinkedIn Masterclass Techweek 2024 v4.1.pptxSymbio Agency Ltd
 
8 Questions B2B Commercial Teams Can Ask To Help Product Discovery
8 Questions B2B Commercial Teams Can Ask To Help Product Discovery8 Questions B2B Commercial Teams Can Ask To Help Product Discovery
8 Questions B2B Commercial Teams Can Ask To Help Product DiscoveryDesmond Leo
 
USA classified ads posting – best classified sites in usa.pdf
USA classified ads posting – best classified sites in usa.pdfUSA classified ads posting – best classified sites in usa.pdf
USA classified ads posting – best classified sites in usa.pdfsuperbizness1227
 
Lookback Analysis
Lookback AnalysisLookback Analysis
Lookback AnalysisSafe PaaS
 
Global Interconnection Group Joint Venture[960] (1).pdf
Global Interconnection Group Joint Venture[960] (1).pdfGlobal Interconnection Group Joint Venture[960] (1).pdf
Global Interconnection Group Joint Venture[960] (1).pdfHenry Tapper
 
Did Paul Haggis Ever Win an Oscar for Best Filmmaker
Did Paul Haggis Ever Win an Oscar for Best FilmmakerDid Paul Haggis Ever Win an Oscar for Best Filmmaker
Did Paul Haggis Ever Win an Oscar for Best Filmmakerstajohn447
 
Understanding UAE Labour Law: Key Points for Employers and Employees
Understanding UAE Labour Law: Key Points for Employers and EmployeesUnderstanding UAE Labour Law: Key Points for Employers and Employees
Understanding UAE Labour Law: Key Points for Employers and EmployeesDragon Dream Bar
 

Recently uploaded (20)

falcon-invoice-discounting-a-premier-platform-for-investors-in-india
falcon-invoice-discounting-a-premier-platform-for-investors-in-indiafalcon-invoice-discounting-a-premier-platform-for-investors-in-india
falcon-invoice-discounting-a-premier-platform-for-investors-in-india
 
State of D2C in India: A Logistics Update
State of D2C in India: A Logistics UpdateState of D2C in India: A Logistics Update
State of D2C in India: A Logistics Update
 
Equinox Gold Corporate Deck May 24th 2024
Equinox Gold Corporate Deck May 24th 2024Equinox Gold Corporate Deck May 24th 2024
Equinox Gold Corporate Deck May 24th 2024
 
Using Generative AI for Content Marketing
Using Generative AI for Content MarketingUsing Generative AI for Content Marketing
Using Generative AI for Content Marketing
 
Byrd & Chen’s Canadian Tax Principles 2023-2024 Edition 1st edition Volumes I...
Byrd & Chen’s Canadian Tax Principles 2023-2024 Edition 1st edition Volumes I...Byrd & Chen’s Canadian Tax Principles 2023-2024 Edition 1st edition Volumes I...
Byrd & Chen’s Canadian Tax Principles 2023-2024 Edition 1st edition Volumes I...
 
Evolution and Growth of Supply chain.pdf
Evolution and Growth of Supply chain.pdfEvolution and Growth of Supply chain.pdf
Evolution and Growth of Supply chain.pdf
 
India’s Recommended Women Surgeons to Watch in 2024.pdf
India’s Recommended Women Surgeons to Watch in 2024.pdfIndia’s Recommended Women Surgeons to Watch in 2024.pdf
India’s Recommended Women Surgeons to Watch in 2024.pdf
 
Easy Way to Download and Set Up Gen TDS Software on Your Computer
Easy Way to Download and Set Up Gen TDS Software on Your ComputerEasy Way to Download and Set Up Gen TDS Software on Your Computer
Easy Way to Download and Set Up Gen TDS Software on Your Computer
 
Special Purpose Vehicle (Purpose, Formation & examples)
Special Purpose Vehicle (Purpose, Formation & examples)Special Purpose Vehicle (Purpose, Formation & examples)
Special Purpose Vehicle (Purpose, Formation & examples)
 
What are the main advantages of using HR recruiter services.pdf
What are the main advantages of using HR recruiter services.pdfWhat are the main advantages of using HR recruiter services.pdf
What are the main advantages of using HR recruiter services.pdf
 
Falcon Invoice Discounting Setup for Small Businesses
Falcon Invoice Discounting Setup for Small BusinessesFalcon Invoice Discounting Setup for Small Businesses
Falcon Invoice Discounting Setup for Small Businesses
 
Business Valuation Principles for Entrepreneurs
Business Valuation Principles for EntrepreneursBusiness Valuation Principles for Entrepreneurs
Business Valuation Principles for Entrepreneurs
 
April 2024 Nostalgia Products Newsletter
April 2024 Nostalgia Products NewsletterApril 2024 Nostalgia Products Newsletter
April 2024 Nostalgia Products Newsletter
 
LinkedIn Masterclass Techweek 2024 v4.1.pptx
LinkedIn Masterclass Techweek 2024 v4.1.pptxLinkedIn Masterclass Techweek 2024 v4.1.pptx
LinkedIn Masterclass Techweek 2024 v4.1.pptx
 
8 Questions B2B Commercial Teams Can Ask To Help Product Discovery
8 Questions B2B Commercial Teams Can Ask To Help Product Discovery8 Questions B2B Commercial Teams Can Ask To Help Product Discovery
8 Questions B2B Commercial Teams Can Ask To Help Product Discovery
 
USA classified ads posting – best classified sites in usa.pdf
USA classified ads posting – best classified sites in usa.pdfUSA classified ads posting – best classified sites in usa.pdf
USA classified ads posting – best classified sites in usa.pdf
 
Lookback Analysis
Lookback AnalysisLookback Analysis
Lookback Analysis
 
Global Interconnection Group Joint Venture[960] (1).pdf
Global Interconnection Group Joint Venture[960] (1).pdfGlobal Interconnection Group Joint Venture[960] (1).pdf
Global Interconnection Group Joint Venture[960] (1).pdf
 
Did Paul Haggis Ever Win an Oscar for Best Filmmaker
Did Paul Haggis Ever Win an Oscar for Best FilmmakerDid Paul Haggis Ever Win an Oscar for Best Filmmaker
Did Paul Haggis Ever Win an Oscar for Best Filmmaker
 
Understanding UAE Labour Law: Key Points for Employers and Employees
Understanding UAE Labour Law: Key Points for Employers and EmployeesUnderstanding UAE Labour Law: Key Points for Employers and Employees
Understanding UAE Labour Law: Key Points for Employers and Employees
 

statistics

  • 2. INDIVIDUAL DISCRET CONTINUOUS S.no Marks Marks Freq. Marks Freq. 1 30 20 8 10 -20 8 2 40 30 12 20 -30 12 3 50 40 20 30 -40 20 4 60 50 10 40 -50 10 5 70 60 6 50 -60 6
  • 3. marks Freq.(f) Cumm.freq.(cf) 20 8 8 30 12 20 40 20 40 50 10 50 60 6 56
  • 4.  Measuresof Central Tendency are used to describe the set of data.  Mean  Median  Mode  
  • 5. 1.Arithmetic Mean 2.Shortcut Method to Mean 3.Direct Method to mean 4.Shortcut Method for Direct Method 5.Calculation of Mean:- *Individual series *Discret series *continuous series
  • 6. Mean The mean is also known as the average of the set. Add all of the number is in the set and divide this sum by the number of items in the set.
  • 7. 1.Easy to understand. 2.Simple to compute. 3. Based on all items. 4.Affected by extreme observation. 5.Capable of further calculation.
  • 8. 1.Arithmetic Mean: X X N X X1 X 2 X 3 ..... Xn N =No. of observations/items in a series x 20 30 10
  • 9.  2. Shortcut method to Mean Ex:- X d= X-A d X A 20 N Assumed mean 30  A d X A 40 50
  • 10.  3.Direct Method:- Marks(X) f fx f x 20 4 X f 30 2 40 3 f N 50 1
  • 11.  4.Shortcut Method for Direct Method:- f d X A f d x A Marks f d = x-A f.d 20 8 30 12 40 20 50 10
  • 12.  Calculation of Mean in Continuous series:- f ( m) X f m mid point of class interval Marks (x) f m f (m) 10 – 20 8 20 – 30 12 30 – 40 20 40 – 50 10 50 - 60 6
  • 13. Since its definition is precise and clear, calculation is easy and its value always determinate.  Its chief merit consists in the fact that it take onto consideration every item in the data.  NO special arrangement of data is necessary while calculating it, unlike median and mode where we have to arrange and group the data in a certain manner.  It forms a good basis of comparison while comparing different groups of numerical data.
  • 14. Omission of even a single item of the data gives an incorrect value of the A.M., unlike median and mode where extreme items can simply be discarded.  It may not identical with any one of the items of the data. That is, it may not be one of the figures that comprise the data.  The fact that it gives a large weight to extreme items is its handicap since it then fails to be a good representatives. That is, the value of A.M. of the data consisting of very and very small items may lead to wrong conclusions.  It cannot be used in qualitative studies, unlike the median.
  • 15. 1.Definition 2.Characteristics 3.Calculating median:- *Individual series *Discret series *Continuous series 4.Advantages & Disadvantages of median.
  • 16.  The value of the middle item of a series that is ordered either in the ascending or descending order of magnitude is called the median. 1.Measure of central tendency marks order marks order 2.Middle value in ordered sequence 40 30  If n is odd, middle 60 value of sequence 20 10  If n is even, average of 50 2 middle values. (n= no 40 of items in a series) 10 20 30 50
  • 17.  Odd series:- middle value of sequence.(series must be in order)  Even series:- median= N 1  th item 2  N No. of observation
  • 18. Arrange the data in ascending or descending order  Find c.f.  Apply N 1 th 2  Look for the value in cf. corresponding figure to cf is the median. Income No. of cf person(f) 800 16 1000 24 1500 26 1800 30 2000 20 2500 6
  • 19. Method:- same as discrete series but instead of N 1 2 N apply 2 to determine the median class. Then apply, N cf Median = L 2 *i f L= lower limit of the median class cf= cf of the class preciding the median class f= frequency of median class i=class interval
  • 20. Marks No.of cf student(f) 0–5 4 N 2 5 – 10 5 N 10- 15 10 cf L 2 *i f 15 – 20 10
  • 21. Most of the conditions of an ideal average are satisfied by it.  The median is of immense use while estimating qualities such as honestly, intelligence, virtue, morality etc. and proves to be a good representative.  It’s possible to find the median by knowing only the values of central items and the no. of items. That is, the values of extreme items are not necessary for finding the median.
  • 22. An irregular series is characterized by extreme variations between the items, in the case of such a series the median fails to be representative.  Arrangement of the data either in the ascending order of the magnitude or descending order is the chief requisite. This process is tedious when the data is vast.  Sometimes the medians may exist between two values, thus involving the work of estimation.  Unlike the A.M., it is not possible to find the total value of all items if we know the value of the median and the no. of items.
  • 23.  QUARTILE:- It divides the entire series into 4 equal parts. Quartiles in:- # Individual & discrete series # Continuous series
  • 24. N 1 Q1 th 4 N 1 Q3 3 th 4 N N Q1 th Q3 3 th 4 4 N N cf 3 cf 4 4 Q1 L *i Q3 L *i f f
  • 25. Find Q1 & Q3 class f cf 0-5 7 5 – 10 18 10 -15 25 15 – 20 30 20 – 25 20
  • 26. The value of the item in a variable that is repeated the greatest number of times is called the mode.
  • 27. The number that repeats the most 3, 4, 4, 10, 15, 16, 18 4 is the mode
  • 28. there may be more than one mode 3, 3, 4, 4, 4, 7, 9, 9, 9 4 & 9 are the modes
  • 29. when there is only single value(f) which is highest. f1 f  M L i 2 f1 f  f 2 L= lower limit of model class f1= frequency of model class fo= frequency of class preciding the model class f2= frequency of class successiding the model class
  • 30. Calculate mode f1 f  marks No. of M L i student 2 f1 f  f 2 0 – 10 10 10 – 20 12 20 – 30 15 30 – 40 8 40 - 50 5
  • 31. When there are two similar frequencies/values which are highest. MODE = 3 MEDIAN – 2MEAN
  • 32. 1.It is the most predominant item in a discrete series. 2.If a continuous series is a regular one i.e. with the maximum frequency in the centre the mode can be calculated easily without knowing the frequencies at the two extremities of the series. 3.It is very useful average in studying business relating to sales, profits etc.
  • 33. 1.It is quite possible that in certain types of data it may not be properly defined & hence it may be indeterminate & indefinite. 2.The value of the mode is not the value obtained by considering the value of every item of the data. 3.In the case of an irregular series it is not very easy to determine the mode. 4.It is quite possible that in certain instances there may be two or more values for the mode.
  • 34. BOOK:- Quantitative Techniques in Business by : Dr. Aditham B.Rao