Ram Deo Statistics

7/30/2019 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

Ram Deo Statistics

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