QUANTITATIVE TECHNIQUES IN MANAGEMENT PDF
Quantitative Techniques for Management. School of Distance Education. Bharathiar University, Coimbatore - MBA First Year. Paper No. 6. PDF | Notes for first year myavr.infouction Engineering and Management. Quantitative methods for management. Engbteenhgand Process Economics 2 () 0 Elsevier Scientific Publishing Company, Amsterdam.
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Tamim_Ansary_Destiny_Disrupted_A_History_of_the(zlibraryexau2g3p_onion). pdf Destiny Disrupted. Quantitative Methods for Business and Management. Quantitative Methods in Management| MSc in Management Quantitative decision-making is the use of mathematical methods and data analysis, as the. Quantitative Techniques in Management,3e. By N. D. Vohra. About this book · Shop for Books on Google Play. Browse the world's largest eBookstore and start .
The use of past data in a systematic manner and constructing it into a suitable model for future use comprises a major part of scientific management. For example, consider a person investing in fixed deposit in a bank, or in shares of a company, or mutual funds, or in Life Insurance Corporation. The expected return on investments will vary depending upon the interest and time period. We can use the scientific management analysis to find out how much the investments made will be worth in the future.
There are many scientific method software packages that have been developed to determine and analyze the problems. In case of non-availability of past data where quantitative data is limited, qualitative factors play a major role in making decisions.
It is unusual to find such a complete list within one book. Each of these techniques is explained using the minimum of mathematics and mathematical jargon.
This makes the book easy to read, and it will not frighten off those interested in business, but not mathematics, as does so much Operations Research literature. Any student having used this book should have an understanding of the various quantitative methods available for use in solving management problems.
However, with such a list of topics, and the intention to provide a readable description, no subject is treated in very much depth. The students would not be adequately prepared to carry out any detailed studies.
For that he would have to go to one of the more standard OR texts which are given as supplernentary reading.
To try to define the depth of treatment, the following examples are cited: Simulation describes the Monte Carlo method, but not methods of variance reduction; in LP: In summary therefore, the book is very suitable for teaching an appreciation of quantitative techniques to non-mathematically inclined students, or for the manager or engineer to read by his fireside, but it is in no way a reference book describing the full potentia!
Let X1. Xn be n observations with respective frequencies f1. Hence Proved Multiplying both sides by fi and taking sum over all the observations. If X denotes simple mean and Xw denotes the weighted mean of the same data. To prove this. This property of arithmetic mean highlights the relationship between X.. If X1 and N1 are the mean and number of observations of a series and X2 and N2 are the corresponding magnitudes of another series. According to this property.. Arithmetic mean is capable of being treated algebraically.
If there are k series each with mean Xi and number of observations equal to Ni. To find mean of the combined series. This property is obvious and requires no proof. Quantitative Techniques for Management Differentiating 1 w. Let X. The respective distributions of their monthly salaries are given in the following table: Measures of Central Tendency Multiply both sides by fi and take sum over all the observations.
Let X be the mean of the observations X1. If every observation is multiplied divided by a constant b. Example 9: There are teachers and non-teaching employees in a college..
Xn with respective frequencies as f1. If some observations of a series are replaced by some other observations. When B is added to every observations. Dividing both sides by N. X3 are replaced by the respective observations Y1. Quantitative Techniques for Management 06 From the above data find: The average rainfall for a week.
Quantitative Techniques in Management,3e
We have to determine the value of X. Let this be X. Due to heavy rainfall on Sunday. How much rainfall was on Sunday? A week can be treated as composed of two groups: Weights No. Students f X -3 2 95 fu 5 12 f1 -2 -1 -6 0 0 14 The following is the distribution of weights in lbs.
Let f1 be the frequency of the class Example The mean age of the combined group of men and women is If the mean age of the sub-group of men is 35 years and that of the sub-group of women is 25 years.
What is Quantitative techniques in Management ?
Find out the missing item x of the following frequency distribution whose arithmetic mean is Let x be the percentage of men in the combined group. Let P denote profit and S denote sales.
The arithmetic mean of 50 items of a series was calculated by a student as Quantitative Techniques for Management X: The sales of a balloon seller on seven days of a week are as given below: Find the correct value of mean.
Calculate the arithmetic mean. The following table gives the monthly income in rupees of families in a certain locality. Measures of Central Tendency Demerits Although. Some demerits of arithmetic mean are: Calculation of arithmetic mean requires simple knowledge of addition.
It can neither be determined by inspection nor by graphical location. Exercise with Hints 1. Simple arithmetic mean gives greater importance to larger values and lesser importance to smaller values.
Arithmetic mean cannot be computed for a qualitative data. It represents the centre of gravity of the distribution because it balances the magnitudes of observations which are greater and less than it. Arithmetic mean is rigidly defined by an algebraic formula. It provides a good basis for the comparison of two or more distributions. To compute mean. It is also simple to understand the meaning of arithmetic mean.
Take the mid-value of a class as the mean of its limits and find arithmetic mean by the step-deviation method. It is too much affected by extreme observations and hence. Arithmetic mean cannot be computed when class intervals have open ends.
In the absence of a complete distribution of observations the arithmetic mean may lead to fallacious conclusions. Calculation of arithmetic mean is based on all the observations and hence. Weights in gms No.
It is capable of being treated mathematically and hence. By stating the necessary assumptions. The value of mean obtained for a data may not be an observation of the data and as such it is called a fictitious average.
It is least affected by the fluctuations of sampling. The frequency distribution of weights in grams of mangoes of a given variety is given below. Arithmetic mean can be computed even if the detailed distribution is not known but sum of observations and number of observations are known. Compute arithmetic mean of the following distribution of marks in Economics of 50 students. This distribution is with open end classes. To calculate mean.
Typist A can type a letter in five minutes. A will type 12 letters. The cost of each kilometre is incurred at the beginning of the kilometre so that the rider pays for the whole kilometre. It is given that there is no student having weight below 90 lbs. What is the average cost of travelling 2 3 kilometres? Total cost of travelling 2 7. This is a less than type cumulative frequency distribution. Determine i Total amount of bonus paid and ii Average bonus paid per employee.
What is the average number of letters typed per hour per typist? In one hour.
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Marks more than 0 10 20 30 40 No. A taxi ride in Delhi costs Rs 5 for the first kilometre and Rs 3 for every additional kilometre travelled. The monthly profits. B will type 6 letters and C will type 4 letters.
The rates of bonus in various salary groups are: Monthly Salary: Profit per Shop: Quantitative Techniques for Management Income: On this assumption the lower limit of the first class will be 0. First convert the distribution into class intervals and then calculate X. Find the frequencies of the classes from the given information. See example Find the number of girls and boys in the class. Find the correct arithmetic mean. By arranging the following information in the form of a frequency distribution.
The mean wage of 60 labourers working in the morning shift is Rs The average daily price of share of a company from Monday to Friday was Rs Take n1 as the no. Percentage Dividend No. Find the mean wage of 40 laboures working in the evening shift. Take class intervals as 0. If an item 13 is replaced by The mean salary paid to employees of an establishment was found to be Rs Rearrange this in the form of frequency distribution by taking class intervals as The mean weight of students in a certain class is 60 kgs.
The mean wage of labourers working in a factory. From the following data. Find the missing frequencies of the following frequency distribution: Find class intervals if the arithmetic mean of the following distribution is Step deviations Frequency Hint: The mean weight of boys in the class is 70 kgs and that of girls is 55 kgs.
The mean of 25 items was calculated by a student as If the highest and lowest price during the week were Rs and Rs respectively. The no. Later on. Then the weighted average of Let x be the percentage of marks in third test.
The average marks of 39 students of a class is Quantitative Techniques for Management Class Intervals: The marks obtained by 40th student are 39 more than the average marks of all the 40 students. Correct average is weighted arithmetic average. The means calculated for frequency distributions I and II were 36 and 32 respectively. Price of a banana is 80 paise and the price of an orange is Rs 1. See example 9. Find the missing frequencies of the two distributions. The following table gives the number of workers and total wages paid in three departments of a manufacturing unit: Department No.
If a person purchases two dozens of bananas and one dozen of oranges. A appeared in three tests of the value of Find mean marks of all the 40 students. Marks obtained by students who passed a given examination are given below: Marks obtained: Average expenditure per family. The following table gives the distribution of the number of kilometres travelled per salesman. Obtain total number of kilometre travelled for each rate of conveyance allowance by multiplying mid-values of column 1 with column 2.
B and C. The difference between actual and average expenditure for each family. Treat this as frequency 'f' and third column as 'X' and find X.
The following table gives distribution of monthly incomes of employees of a firm: Income in Rs ' The details of monthly income and expenditure of a group of five families are given in the following table: A company has three categories of workers A. The more incidence of disease is given by higher average number of patients. Justify your conclusion. Would you regard this as a typical wage?
Explain Hint: An average that is representative of most of the observations is said to be a typical average. Median is a positional average because its value depends upon the. If his average sales of the first three quarters is Rs Since the weight of the largest wage is less in In terms of frequency curve. Would you regard this mean as typical of the salaries? Find the marginal cost of the 11th unit.
During the following year. Compute their mean salary. During The number of patients visiting diabetic clinic and protein urea clinic in a hospital during April If a male worker earns Rs per day and a female worker earns Rs. On the basis of the method given above. Writing the observations in ascending order.
Consider the observations: Arranging these observations in ascending order of magnitude. Measures of Central Tendency Determination of Median a When individual observations are given The following steps are involved in the determination of median: Here we may note that only 3 observations are below 17 and 4 observations are above it and hence.
Based on this definition.
Find median of the data: In order to avoid this ambiguity. The same value of Md will be obtained by arranging the observations in descending order of magnitude.. Find median of the following observations: Median of a distribution is that value of the variate such that at least half of the observations are less than or equal to it and at least half of the observations are greater than or equal to it. According to the above definition of median.
Looking at the frequency distribution we note that there are observations which are less than or equal to 4 and there are By convention we take the middle value of the interval as median. In such a case. Alternative Method: Locate median of the following frequency distribution: From the table 48th observation is From the table we note that th observation is 4 and th observation is 5.
Variable X: Classes Frequency: Classes 1 0. Suppose we wish to find the median of the following frequency distribution. Such a histogram is shown below: Histogram Figure: Measures of Central Tendency c When grouped frequency distribution is given Interpolation formula The determination of median. The median of a distribution is that value of the variate which divides the distribution into two equal parts. We may note here that area under each rectangle is equal to the frequency of the corresponding class.
Let the point. Writing the given data in a tabular form. The position of this point In case of a grouped frequency distribution. Quantitative Techniques for Management should be such that the ordinate AMd in the above histogram divides the area of median rectangle so that there are only Since the variable.
From the histogram.. Applying this formula to the above example. Equation 2 gives the required formula for the computation of median. Determination of Median When 'greater than' type cumulative frequencies are given By looking at the histogram.
Lm is lower limit. The above formula is also applicable when classes are of unequal width. Calculate median of the following data: Height in inches: Let U m be the upper limit of the median class. Median can be computed even if there are open end classes because here we need to know only the frequencies of classes preceding or following the median class..
The weekly wages of 1. Obtain median of the given data. The following table gives the distribution of marks by students in an examination. Weekly Wages less than: Class Intervals Class Intervals less than Calculate median.
Since the class intervals are inclusive. The above is a 'less than' type frequency distribution. The calculations of X and Md are shown below: Class Intervals 0. On substituting various 2 values in the formula for median. Note that it is 'greater than' type frequency distribution. Find the median of the following data: Age greater than in yrs: Calculate mean and median. The following table gives the daily profits in Rs of shops of a town.
Find median of the following distribution: On subtracting and adding half of this. Measures of Central Tendency Values Frequency: Since the mid-values are equally spaced. Wages Rs: This width is 1. Let f1 and f2 be the frequencies of the classes The following table gives the distribution of daily wages of workers.
Class Intervals Frequency c. After this.
Values Class Intervals Frequency c. If the median of the distribution is Rs Class Intervals Frequency 0. Locate the median of the above data using i only the less than type ogive. Drop a perpendicular from S.
The following table shows the daily sales of footpath sellers of Chandni Chowk: Sales in Rs No. The point at which this meets X. To draw ogives. Quantitative Techniques for Management Graphical location of Median So far we have calculated median by the use of a formula.
It is a positional average. Set I: Median is used to convey the idea of a typical observation of the given data. It is not based on the magnitudes of all the observations. A perpendicular is dropped from the point of intersection of the two ogives. In case of individual observations. It is obvious from Fig.
Uses 1. This assumption is rarely met in practice. Measures of Central Tendency Properties of Median 1. Median can be determined even when class intervals have open ends or not of equal width. Median can also be located graphically. This property implies that median is centrally located. Since it is not possible to define weighted median like weighted arithmetic mean.
It can be shown that the sum of absolute deviations is minimum when taken from median. The formula for the computation of median. In such cases it can even be located by inspection. Merits and Demerits of Median a Merits 1. Median is the most suitable measure of central tendency when the frequency distribution is skewed. It is an appropriate measure of central tendency when the characteristics are not measurable but different items are capable of being ranked.
Median conveys the idea of a typical observation. It is the only suitable average when data are qualitative and it is possible to rank various items according to qualitative characteristics. It is not much affected by extreme observations. It is easy to understand and easy to calculate. When the given data has class intervals with open ends. Median is often computed when quick estimates of average are desired. The point at which it intersects the X-axis gives median.
There may be a situation where different sets of observations give same value of median. It is centrally located measure of average since the sum of absolute deviation is minimum when taken from median. In comparison to arithmetic mean.
Quantitative Techniques for Management
It is also independent of range or dispersion of the data. For a continuous or grouped frequency distribution. It is also possible to divide it into more than two equal parts. The values that divide a distribution into more than two equal parts are commonly known as partition values or fractiles.
After locating the first quartile class. For a grouped frequency distribution. The formula for the computation of Q1 can be written by making suitable changes in the formula of median. Since three values are needed to divide a distribution into four parts. Some important partition values are discussed in the following sections.
The third quartile Q3 of a distribution can also be defined in a similar manner. For a discrete distribution. Quartiles The values of a variable that divide a distribution into four equal parts are called quartiles.
By definition. Find Arithmetic mean of first ten prime numbers. Q2 and Q3. LQ1 is lower limit of the first quartile class. Deciles Measures of Central Tendency Deciles divide a distribution into 10 equal parts and there are P99 respectively.. P60 and P90 from the following data: Daily Profit in Rs: First we calculate the cumulative frequencies. The corresponding formulae based on 'greater than' type cumulative frequencies can be written in a similar manner.
D9 respectively. U PK are the upper limits of the corresponding classes and C denotes the greater than type cumulative frequencies. Locate Median Determination of D4 and D7: From the cumulative frequency column. Substituting these values in the formula for median. Wages per Week in Rs No. From 4 the cumulative frequency column. First we make a cumulative frequency distribution table: P60 and P Determination of P Also determine i The percentage of workers getting weekly wages between Rs and Rs and ii percentage of worker getting wages greater than Rs Determination of Q1 and Q3: First we determine N which is equal to Since lies in the class The 70th percentile class is The 40th percentile class is Let x be the percentage of workers getting wage less than For Q1.
Using the formula for xth percentile we have x. Using the relevant formula. The sixth decile class is 10 The third quartile class is 4 The first quartile class is 4 The third decile class is 10 Let X1.
The monthly profits in Rs of shops are distributed as follows: This is a 'less than' cumulative frequency distribution.. However, with such a list of topics, and the intention to provide a readable description, no subject is treated in very much depth. Discuss the scope and significance of the study of statistics. Find median of the data: Let f1 and f2 be the frequencies of the classes This does not mean that they have to be expert mathematicians, but they must have a basic understanding of the principles.
Then in later years the subject was developed by Abraham De Moivre
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