SEMESTER-2
ASSIGNMENT
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BUSINESS STATISTICS
1- Correlation-
Correlation 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
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.
Regression-
Regression 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.
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
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 tendency-
1) 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
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 dispersion-
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
3.A) Independence of events-
In 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
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.
