Ram Deo Statistics
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Transcript of Ram Deo Statistics
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BUSINESS STATISTICSMEAN , MEDIAN AND
MODE
Submitted to:- Mrs. RuchikaFMS Dept.
NIFT,
JodhpurSubmitted By:- Ram Deo Bharti
MFM 1st SEMESTER
NIFT, JODHPUR
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MEAN
Mean is a value obtained by adding together
all the observation and by dividing this total
by the number of observation.
The mean is the mathematical average of a set
of numbers.
The mean is calculated by adding up two or
more scores and dividing the total by the
number of scores.
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FORMULA OF MEAN
A.M = X1+X2+X3+X4+X5++Xn
N
Formula of Mean for ungrouped data=
X= Elements.N= Total no. of observation.
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Indirect method forgrouped Data
A-Mid point of entry of middle class.
f- Frequency
N- Total Observation
d- Deviation
C- Size of equal interval.d = X - A
c
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OBJECTIVE Of MEAN
To get single value that describes the
characteristics of whole data.
To facilitate comparison of point of time or
over period of time.
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CHARACTERISTICS OF MEAN
It is for understanding.
It is simple for computing.
It is based on all observation.
Capable of further algebraic treatment.
It have sampling stability.
It is rigidly defined.
It is unduly affected by the presence ofextreme values.
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MERIT OF MEAN
Arithmetic mean rigidly defined by algebric
formula.
It is easy to calculate and simple to understand.
It is based on all observations and it can be
regarded as representative of the given data.
It is capable of being treated mathematically
and hence it is widely used in statistical
analysis.
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CONTINUED
Arithmetic mean can be computed even if the
detailed distribution is not known but some of
the observation and number of the observation
are known.
It is least affected by the fluctuation of
sampling.
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DEMERITS OF MEAN
It can neither be determined by inspection or
by graphical location. Arithmetic mean cannot be computed for
qualitative data like data on intelligence
honesty and smoking habit etc. It is too much affected by extreme
observations and hence it is not adequately
represent data consisting of some extremepoint.
Arithmetic mean cannot be computed when
class intervals have open ends
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MEDIAN
The median is the measure of central tendency
which appears in the middle of an ordered
sequence of values.
The numerical value separating the higher half
of a sample, a population, or a probability
distribution, from the lower half.
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Formula of Median
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FORMULA OF MEDIAN
MEDIAN IS ALWAYS IN SIZE OF n+1/2th TERM.
L = Lower limit of median class.
F = Preceding cumulative frequency of median class.
N = Total no. of elements.I = Class interval.
f = Frequency of median class.
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GRAPHICAL PRESENTATION OF
MEDIANAxis X represents no of
marks obtained by students
and Axis Y represents no of
students..Less than Curve
and more than curve
intersects each others at A,hence perpendicular drawn
from A cuts X axis at A, so
Median is approx 443.5..
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MERITS OF MEDIAN It is easy understand and to easy to calculate
It can easy to find out by inspection
Median can be determined even when classintervals have open ends
It is not much affected by extreme observationsand also interdependent of range or dispersionof the data
Median can also be located graphically
It is only suitable average when the data arequalitative & it is possible to rank various itemsaccording to qualitative characteristics.
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DEMERITS OF MEDIAN
In case of individual observations the process
of locations of median requires their
arrangement in order of the magnitude which
may be cumbersome task
It is being a positional average it is not capable
treated algebraically
It not based on the magnitude of all the
observations
in comparison to arithmetic mean it much
affected by the fluctuations of sampling
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MODE The modal value of a set of data is the most
frequently occurring value.
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MERITSOF MODE
It is easy to understand and easy to calculate.In many cases it can be located just byinspection
Like mean or median it is not affected by
extreme observations
It can be determined even if distribution hasopen end classes
It is value around which more concentrationsof observations and hence the bestrepresentative of data.
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DEMERITSOF MODE
It is not based on all observations It is not capable of further mathematical
treatment
It is much affected by fluctuations ofsampling
It is not suitable when different items of data
are unequal importance.
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GRAPHICAL PRESENTATION OF MODE
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1.Draw a histogram of the given data.
2. Draw two lines diagonally inside of the modalclass bar.
3. Draw a perpendicular line from the intersection ofthe two diagonal lines to the X-axis, which gives usthe modal value.
Profits (in Rs.Lakhs) No.Of Shops
0-100 15100-200 23
200-300 34
300-400 25
400-500 21
500-600 8
RELATIONSHIP AMONG MEAN
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RELATIONSHIP AMONG MEAN,
MEDIAN AND MODE
Empirical relation between Mean, Median andMode:
The relationship between mean, median and
mode depends upon the nature of the distribution.
A distribution may be symmetrical or
asymmetrical.
In asymmetrical distribution the mean,
median and mode are equal
i.e. Mean(AM) = Median(M) =
Mode(Mo)
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In a highly asymmetrical distribution it is not
possible to find a relation ship among the
averages. But in a moderately asymmetric
distribution the difference between the meanand mode is three times the difference between
the mean and median.
i.e. Mean-Mode =3(Mean-Median)
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Mean-Median = 1 (Mean- Mode)
3Or, Mode = 3 Median2 Mean
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THANKS