SEMESTER 2 ASSIGNMENT BUSINESS STATISTIC

SEMESTER-2

ASSIGNMENT –BUSINESS STATISTICS
1- CorrelationCorrelation is a measurement of how two variables are related to each other and it can
range from positive one to negative one levels. In the correlation both the variables are
observed as they naturally occur since neither variable can be fixed at predetermined
levels. Correlation is an analysis of the co variation between two or more variables.
Correlation is a degree of linear association between two random variables. In correlation
one is cause and other is effect. Independent or dependent variables. Correlation is a
degree of linear association between two random variables. Correlation analysis helps to
identify relationship of various factors and decision variables. A correlation considers the
joint variation of two measurements with no distinctions as dependent and independent
variables. It is a measure of linear relationship between them to understand the whole
analysis. To understand the relation of various type of things and factors and decision
variables it helps to the management to take a better decision. To calculate a value on
guess trial of one variable for a given value of other if both are related to each other
likewise estimating the sales activities for marketing like advertising and promotion of
the product. It helps in understanding the market behaviour as well as economic
behaviour. It also help and improve the uncertainty in decision making process to a large
extent. The correlation is said to be positive when up and down or increase and decrease
in the value of one variable is accompanied by increase and decrease in the value of

other variable also . In simple correlation is the variation among or between only two
variables understudy and the variation is hardly influenced by any external force or any
term(factor). In other words if one variable remains same then there would be no change
in other variable. When the amount of change in one variable tends to go on a constant

rate of or constant ratio to the amount of change in the other variable , then the
correlation is called or said to be linear. But if the amount of change in one variable does
not consume a constant ratio to the amount of change in the other variable then the
correlation is said to be non linear.
RegressionRegression models do not make decisions for people. Regression models are a source of
information about the world. In order to use them wisely it is important to understand
how they work. Regression is a measurement of the average relationship between two or
more variables in terms of the original units of data. Regression analysis is a branch of
statistical theory which is widely used in all the scientific disciplines. It is basic technique
for measuring or estimating the relationship among economic variables that continues the
essence of economic theory and economic life. Regression provides us a measure of the
relationship and also facilitates to predict one variable for a value of other variable. The
uses of regression analysis are not confined or bound economic and business activities.
Its operation and applications are spread to all most or extended to all most all the
natural, social and physical sciences. Correlation analysis indicates whether two variables

fluctuate with any relationship or not. Regression provides us a measure of the
relationship and also facilitates to predict or foresaid one variable for a value of the other
variable. Although, unlike correlation analysis or research , in regression analysis, one
variable is independent and other dependent. Thus the regression analysis or research
only gives a mathematical measure of average relationship between two variables. This is
one of the most commonly used statistical tool for predictions or forecast of economic
and business information for decision making.
In the regression analysis we need to have statistical model that will extract information
from the given data to establish the regression relationship between independent and
dependent relationship. The model should capture systematic behaviour of data. The nonsystematic behaviour cannot be captured and called as errors. The error is due to random
component that can not be predicted as well as the component not adequately considered
in statistical model. Good statistical model captures the entire systematic component
leaving only trash out. If we attempt to capture or catch everything which is systematic in
datasheet . Random errors can not be caught in any situation. If we assume or take an
assumption the random errors are normally divided we can highlight the confidence level
and interval of random errors. Thus, our calculations or analysis are more trustworthy and
faithful. If the variables in a bivariate division are correlated, the points in spread figure
considered near to exact value of the outcome or cluster around some bent. If the figure
or bent is straight line then we can say that it is linear regression. Otherwise it is called
curvilinear regression. The equation of the curve which is closest to observations is called

the best fit. The best fit is calculated or estimated through legender’s principle of least

some squares of deviations of the observed data points from the corresponding outcome
on the best fir curve. This is called minimum squared error criteria. Regression analysis is
one of the most popular and commonly used statistical tools in business. It provides
mathematical relationship between two or more variables. This mathematical can then be
further utilized and analyzed. Most wide use of regression analysis is of course estimation
or calculation and prediction. Some of the common examples are demand and supply,
money supply and expenditure, inflation and interest rates, promotion expenditure and
sales , productivity and profitability, health of workers and absenteeism. The term
regression first came into existence in 1877 when Sir Francis analyzed the relationship
between the height of fathers and sons. His analysis revealed a very interesting
relationship. All tall fathers tend to have tall sons and all short fathers short sons but the
average height of the sons of a group of tall fathers was less than that of fathers and the
average height of the sons of a group of short fathers was greater than that of the fathers.
The line describing or explaining this tendency of going back is called regression line.

2) The concept of central tendency plays an important role in the study for analyzing
some statistical data. This whole data based analysis concentrate the values around a
central part of distribution is called central data. It helps in many ways to take many

decision concerning the entire data analysis. Measure of central tendency acknowledges
us to get an idea of entire analysis. From a single value at which we consider the entire
data is concentrated measure of central tendency also enables us to differentiate between
two or more set of data analysis. Common measures for central tendency1) Mean
2) Median
3) Mode
The shape and size of the distribution of values is reflected in the
relation between the average or difficult values in that distribution. The word average
itself can be very difficult to elaborate the meaning because there are three different
output measures that can be further used to define the average or difficult values in the
distribution of values. The primary motive of each measure of average is to know a
value that might appropriately express the difficult outcome or value of that analyzed
data. In general, these measures recognize a point adjacent the center of the distribution.
Therefore, these measures have been called or by we know them very well measures of
central tendency. These measures of central tendency are the mean, median, and mode. In
the above given problem a measure of central tendency for income of persons who have
boarded a particular train on a particular date at the originating station can be easily
measured by using mean , median and mode methods. Measures of the central tendency
give one of the very important characteristics of the data. According to the above given
problem those passengers who have boarded the train on a particular date, one of the

various measures of central tendency may be selected as the most representative.
Likewise arithmetic mean is widely used and understandable. Mean summarizes all the
information in the given data or datasheet . Mean can be understood or visualized as a
single point where all the mass or weight of the observations in focused. It just like the
law of center of gravity in physics given Newton. Mean also has some desirable
mathematical terms and properties that make it useful in the business statistics. Median is
the best average in open end distributions or in distributions in which it gives highly type
of frequency (skew type, j or reverse j type) . In such events arithmetic mean gives some
undesirable high or low value while median gives more expressed value. Mode is also
useful to describe qualitative data. In general if we go and rate all the methods then
arithmetic mean is the best of all averages as it fulfills almost all the desires and
requirements of an ideal measure of central tendency and other averages are used under
other situations and conditions. The mode is most fashionable size in order to express or
understand that it is the most common and difficult and is defined by Zizek as the value
occur most frequently in series of items and around which the other items are divided
most densely. On other well said by some great man’s the mode of a distribution is the

value at the point where the things tend to most heavily focused. Mode is the value or
outcome which has the greater frequency density in its immediate surrounding.
Although each measure of central tendency attempts to acknowledges the most difficult

value in that distribution of values or outcome, each measure has its own meaning of the
most difficult value. The mean defines central tendency as the mathematical average of
all the values (a measure that you are very familiar with. The median defines central
tendency as the point where it divides ½ the values or outcome fall upon that value and
1/2 the scores fall below it.
A measure of dispersion brief us an idea about the actual extent of lack of uniformity in
the structure, sizes and qualities of the items in the series. It acknowledges us to know the
amount of uniformity and consistency in the series. A measure of dispersion or the way it
varies in any data shows that extent to which the numeric value tend to relocate about an
average. Simplest meaning of dispersion that can be attached to the dispersion is a lack of
singleness in the structure or quantity of the commodity of a group or series. The word
dispersion’s simple meaning is that to spread the analyzed data. A exact measure of
dispersion is the one which gives the outcome or the magnitude of the variation in the
series. It measures in numerical terms the extent of the spread of the values or outcome
around the average. Measures of dispersion1) The range
2) The quartile deviation
3) The median deviation
4) The mean deviation
5) The standard deviation
6) Graphical method

The measures of dispersion can be either absolute or relative. Absolute measures of
dispersion are represented in the same unit in which the original form of outcome or
data are expressed. With the help of Range we can study thoroughly dispersion.
Without wasting too much or we can say it computes the absolute and relative range
very quick. It is very helpful in this given problem as there is variations and quality so
we can well measure the dispersion with the help of range. If we go through the
second method of measure the dispersion quartile deviation is the average of the
difference between top quartile and bottom quartile. The mean deviation is the
arithmetic mean of the absolute deviations of the values about their arithmetic mean
or median or mode. In the given problem there is also an advantage of taking
deviations from the median, because mean deviation from median is lowest as
compared to any other mean deviations because absolute outcome or values of
deviations ignoring sign are taken for calculating mean deviation the mean deviation
is not amenable to further algebraic.

3.A) Independence of eventsIn the independence of the events if two events or two incidents are said to be or called
independent of each other if and only if they follow three conditions:
 P(AB)= P(A) x P(B)
 P(A|B)= P(A)
 P(B|A)=P(B)

We can elaborate in other words If two events are not dependent or independent,
if on the occurrence of the one event does not change the probability of other
event. Like wise if we take an example of the toss of coin the first coin gets
(head/tails) then it would not decide or modify the probability of the second toss
landing tails. So both of these events are independent to each other. This is called
independence of the events. If we take an example of a dice which six faced if it
shows even number we call it event P or if we get odd number we call it odd. So
in this example if we get got odd and even numbers then it is independence of
events.
Mutually Exclusive Events- The two events A and B are considered as mutually
exclusive events if they have no output of the experiment common to them. In
other words the event A and event B are said to be mutually exclusive events if A
intersection B shows a result or zero outcome where the outcome is observed to
be a empty set or called as null. If we talk about a scheduled flight which has to
arrive on time but due to bad weather there are two possibilities that either the
flight can be delayed or canceled both the events can not be done simultaneously.
So this is called mutually exclusive events. If we take another fine example of a
person who is a office going if he arrives office late due to traffic or some other
reasons or he is absent on a some particular occasion then both of these events are
mutually exclusive since both cannot happen together.

3.B) If we have to arrange the letters of the word “MADAM” then we shall have to
calculate the value of some factorials so,
Total letters in the word are 5 so we shall have to go through permutation
 5! Then the value of
5!= 5*4*3*2*1
= 120
But the word MADAM has two M and two A so it will also be considered in the form of
permutation so the possible ways of arranging of the letters of the word “MADAM”
becomes= 5! / 2!* 2!
= 30
So there are 30 possible ways in which we can arrange the letters.