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manash,mba 1st semester 2012

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Spring 2012 Master of Business Administration- MBA Semester 1 MB0040 Statistics for Management - 4 Credits (Book ID: B1129) Assignment Set - 1 (60 Marks) *Note: Each question carries 10 Marks. Answer all the questions.

Q1. What are the functions of Statistics? Distinguish between Primary data and Secondary Data. Ans: Functions of Statistics Statistics is used for various purposes. It is used to simplify mass data and to make comparisons easier. It is also used to bring out trends and tendencies in the data as well as the hidden relations between variables. All this helps to make decision making much easier. Let us look at each function of Statistics in detail. 1. Statistics simplifies mass data The use of statistical concepts helps in simplification of complex data. Using statistical concepts, the managers can make decisions more easily. The statistical methods help in reducing the complexity of the data and consequently in the understanding of any huge mass of data. Example: Fifty people were interviewed to rate a regional movie on the scale of 1 to 10, with number 1 being for the top movie and number 10 being for the worst movie. The table 1a shows the ratings given by 50 customers. Simplify the data? Table 1a The ratings (scale of 1 to 10) for a Regional movie given by 50 customers 157687534712587474249872 5 457987896723287635763954 8

The data in table 1a can be condensed and is presented in table 1b using the statistical concepts such as calculating frequency and frequency distribution to draw conclusions and then frequency table is prepared. In this example, from the bulk data consisting of 50 rating scores, the frequency table was prepared. The frequency table is in condensed and simple form. From the tabled data, we can easily interpret that for the regional movie, most of the customers gave a 7 rating (that is, 11 customers). Only two customers gave a rating of 1 for the regional

movie, which means only two out of 50 customers surveyed liked the regional movie the most. Table 1b Frequency table Rating Frequency 1 2 2 5 3 4 4 6 5 7 6 4 7 11 8 7 9 4 10 0 Total 50

Frequency Distribution 2/50 = 0.04 5/50 = 0.10 4/50 = 0.08 6/50 = 0.12 7/50 = 0.14 4/50 = 0.08 11/50 = 0.22 7/50 = 0.14 4/50 = 0.08 0/50 =0 1

2. Statistics makes comparison easier Without using statistical methods and concepts, collection of data and comparison cannot be done easily. Statistics helps us to compare data collected from different sources. Grand totals, measures of central tendency, measures of dispersion, graphs and diagrams, coefficient of correlation all provide ample scopes for comparison. Hence, visual representation of numerical data helps you to compare the data with less effort and can make effective decisions. 3. Statistics brings out trends and tendencies in the data After data is collected, it is easy to analyse the trend and tendencies in the data by using the various concepts of Statistics. 4. Statistics brings out the hidden relations between variables Statistical analysis helps in drawing inferences on data. Statistical analysis brings out the hidden relations between variables. 5. Decision making power becomes easier With the proper application of Statistics and statistical software packages on the collected data, managers can take effective decisions, which can increase the profits in a business.

The differences between primary and secondary data are listed below: Primary Data 1. Data is original and thus more accurate and reliable. 2. Gathering data is expensive. 3. Data is not easily accessible. 4. Most of the data is homogeneous.

5. Collection of data requires more time. 6. Extra precautionary measures need not be taken. 7. Data gives detailed information. Secondary Data 1. Data is not reliable. 2. Gathering data is cheap 3. Data is easily accessible through internet or other resources. 4. Data is not homogeneous. 5. Collection of data requires less time. 6. Data needs extra care. 7. Data may not be adequate. Q2. Draw a histogram for the following distribution: Age No. Of people 0-10 5 10-20 10 20-30 15 30-40 8 40-50 2

Histogram showing following data

Q3. Find the median value of the following set of values: 45, 32, 31, 46, 40, 28, 27, 37, 36, 41. Ans: Arranging in ascending order, we get: 27,28,31,32,36,37,40,41,45,46 We have, n=10 Therefore, Median=(10+1) th /2 Value=5.5th M=(36+37)/2 =73/2 = 36.5 The median for the given set of values is 36.5 Q4. Calculate the standard deviation of the following data: Marks 78-80 80-82 82-84 84-86 86-88 88-90 No. of 3 15 26 23 9 4 students Ans: The table below represents the frequency distribution of data required for calculating th standard deviation. Class interval 78-80 80-82 82-84 84-86 86-88 88-90 Mid value x 79 81 83 85 87 89 FrequencyF D=x-83 2 3 -2 15 -1 26 0 23 1 9 2 4 3 80 Fd -6 -15 0 23 18 12 32 Fd^2 12 15 0 23 36 36 122

=

=[122/80-[32/80]^2]X(2)^2 =[1.525-0.16]x4 =5.46(mm) =Variance

Standard deviation=

=2.336(mm)

Q5. An unbiased coin is tossed six times. What is the probability that the tosses will result in: (i) exactly two heads and (ii) at least five heads Ans: Let A be the event of getting head. Given that:

(i) The probability that the tosses will result in exactly two heads is given by:

Therefore, the probability that the tosses will result in exactly two heads is 15/64.

(ii) The probability that the tosses will result in at least five heads is given by:

Therefore, the probability that the tosses will result in at least five heads is 7/64. Q6. Explain briefly the types of sampling. Ans: There are two types of sampling. They are briefed as follows: a) Probability Sampling: it provide a specific technique of drawing samples from the population. The technique of drawing sampoles is according to the law which unit has a predetermined probability of being included in the sample. The different ways if assingning probability are : i) each unit has the same chance of being selected. ii) Sampling units have varying probability. iii) Units have probability proportional to the sample size. b) Non-probability sampling: depending upon the object of inquiry and opther considerations a predetermined number of sample units is selected proposely so that they represents the true characteristics of the population. A serious drawback of the sampling design is that it is highly subjective in nature. The selection of sample units depends entirely upon the personal convenience, biases, prejudices and beliefs of the investigator. This method will be more successful if the investigator is thoroughly skilled and experienced.

Spring 2012 Master of Business Administration- MBA Semester 1 MB0040 Statistics for Management - 4 Credits (Book ID: B1129) Assignment Set - 2 (60 Marks) *Note: Each question carries 10 Marks. Answer all the questions. Q1. Explain the following terms with respect to Statistics: (i) Sample, (ii) Variable, (iii) Population. Ans: (i) Sample In statistics, a sample is a subset of a population. Typically, the population is very large, making a censor a complete enumeration of all the values in the population impractical or impossible. The sample represents a subset of manageable size. Samples are collected and statistics are calculated from the samples so that one can make inferences or extrapolations from the sample to the population. This process of collecting information from a sample is referred to a sampling. A complete sample is a set of objects from a parent population that includes ALL such objects that satisfy a set of well-defined selection criteria. For example, a complete sample of Australian men taller than 2m would consist of a list of every Australian male taller than 2m. But it wouldn't include German males, or tall Australian females, or people shorter than 2m. So to compile such a complete sample requires a complete list of the parent population, including data on height, gender, and nationality for each member of that parent population. In the case of human populations, such a complete list is unlikely to exist, but such complete samples are often available in other disciplines, such as complete magnitude-limited samples of astronomical objects. An unbiased sample is a set of objects chosen from a complete sample using a selection process that does not depend on the properties of the objects. For example, an unbiased sample of Australian men taller than 2m might consist of a randomly sampled subset of 1% of Australian males taller than 2m. But one chosen from the electoral register might not be unbiased since, for example, males aged under 18 will not be on the electoral register. In an astronomical context, an unbiased sample might consist of that fraction of a complete sample for which data are available, provided the data availability is not biased by individual source properties. The best way to avoid a biased or unrepresentative sample is to select a random sample, also known as a probability sample. A random sample is defined as a sample where each individual member of the population has a known, non-zero chance of being selected as part of the sample Several types of random samples are simple random samples, systematic samples, stratified random samples, and cluster random samples. (ii) Variable A variable is a characteristic that may assume more than one set of values to which a numerical measure can be assigned. Height, age, amount of income, province or country of birth, grades

obtained at school and type of housing are all examples of variables. Variables may be classified into various categories, some of which are outlined in this section. Categorical variables: A categorical variable (also called qualitative variable) is one for which each response can be put into a specific category. These categories must be mutually exclusive and exhaustive. Mutually exclusive means that e

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