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Mb0040 Q1. (a) Statistics is the backbone of decision-making. Comment.Mar 012011

Answer:

a. Due to advanced communication network, rapid changes in consumer behaviour, varied

expectations of variety of consumers and new market openings, modern managers have a difficult

task of making quick and

appropriate decisions. Therefore, there is a need for them to depend more upon quantitative

techniques like mathematical models, statistics, operations research and econometrics.

Decision making is a key part of our day-to-day life. Even when we wish to purchase a television, we

like to know the price, quality, durability, and maintainability of various brands and models before

buying one. As you can see, in this scenario we are collecting data and making an optimum

decision. In other words, we are using Statistics.

Again, suppose a company wishes to introduce a new product, it has to collect data on market

potential, consumer likings, availability of raw materials, feasibility of producing the product. Hence,

data collection is the back-bone of any decision making process.

Many organisations find themselves data-rich but poor in drawing information from it. Therefore, it is

important to develop the ability to extract meaningful information from raw data to make better

decisions. Statistics play an important role in this aspect.

Statistics is broadly divided into two main categories. Below Figure illustrates the two categories.

The two categories of Statistics are descriptive statistics and inferential statistics.

Descriptive Statistics: Descriptive statistics is used to present the general description of data which

is summarised quantitatively. This is mostly useful in clinical research, when communicating the

results of experiments.

Inferential Statistics: Inferential statistics is used to make valid inferences from the data which are

helpful in effective decision making for managers or professionals.

Statistical methods such as estimation, prediction and hypothesis testing belong to inferential

statistics. The researchers make deductions or conclusions from the collected data samples

regarding the characteristics of large population from which the samples are taken. So, we can say

Statistics is the backbone of decision-making.

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Q2. a) Inclusive and Exclusive limits.

Answer:

Class intervals are of two types; exclusive and inclusive. The class interval that does not include

upper class limit is called an exclusive type of class interval. The class interval that includes the

upper class limit is called an inclusive type of class interval.

Example:

In above table, the class 0 9 includes the value 9.

In above table, the the class 0 10 does not include the value 10. If the value of 10 occurs, it is

included in the class 10 20.

b)MB0040 Q2 b. Continuous and discrete dataMar 052011

(b) : A variable that assumes all the values in the range is known as

continuous variable. A variable that assumes only some specified values in a given range is known

as discrete variable.

For example,

the number of children per family and number of petals in a flower are examples of discrete

variables. The height and weight of persons are examples of continuous variables.

(c) Qualitative and Quantitative data : Data may come from a population or from a sample. Small letters like x or y generally

are used to represent data values. Most data can be put into the following categories:

Qualitative

Quantitative

Qualitative data

Qualitative data are the result of categorizing or describing attributes of a population. Hair color, blood type, ethnic group,

the car a person drives, and the street a person lives on are examples of qualitative data. Qualitative data are generally

described by words or letters. For instance, hair color might be black, dark brown, light brown, blonde, gray, or red. Blood

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type might be AB+, O-, or B+. Qualitative data are not as widely used as quantitative data because many numerical

techniques do not apply to the qualitative data. For example, it does not make sense to find an average hair color or blood

type.

Quantitative data

Quantitative data are always numbers and are usually the data of choice because there are many methods available for

analyzing the data. Quantitative data are the result of counting or measuring attributes of a population. Amount of money,

pulse rate, weight, number of people living in your town, and the number of students who take statistics are examples of

quantitative data. Quantitative data may be either discrete or continuous.

All data that are the result of counting are called quantitative discrete data. These data take on only certain numerical

values. If you count the number of phone calls you receive for each day of the week, you might get 0, 1, 2, 3, etc.

Example 2: Data Sample of Quantitative Continuous Data

The data are the weights of the backpacks with the books in it. You sample the same five students. The weights (in pounds)

of their backpacks are 6.2, 7, 6.8, 9.1, 4.3. Notice that backpacks carrying three books can have different weights. Weights

are quantitative continuous data because weights are measured.

d) (d) Class limits and class intervals:

A continuous frequency distribution is divided into mutually exclusive sub ranges called class-

intervals. Class intervals have lower and upper limits

known as lower class limits and upper class limits respectively. The differences between upper class

limit and lower class limit is termed as class width. The middle value of a class interval is called mid-

value of the class. It is the average of class limits.

3. Q3. In a management class of 100 students three languages are offered as an additional

subject viz. Hindi, English and Kannada. There are 28 students taking Hindi, 26 taking English and

16 taking Kannada. There are 12 students taking both Hindi and English, 4 taking Hindi and

Kannada and 6 that are taking English and Kannada. In addition, we know that 2 students are

taking all the three languages.

i) If a student is chosen randomly, what is the probability that he/she is not taking any of thesethree languages?ii) If a student is chosen randomly, what is the probability that he/ she is taking exactly onelanguage?

Answer:

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a) Our sample space is all the students in the school. There are 100 students, so the size of our samplespace is 100.Our event is that a student drawn at random is not taking any language classes. Call this event A

P(A) = the number of ways A could happen / the size of the sample space

= the number of students taking no language class / 100

So we must find the number of students who are not taking any language class.Let H be the number of students taking Hindi, E be the number of students taking English , and K be thenumber of students taking Kannada.We draw a Venn diagram

Q4. List down various measures of central tendency and explain the difference between them?

Answer:Graphical representation is a good way to represent summarised data. However, graphs provide us onlyan overview and thus may not be used for further analysis. Hence, we use summary statistics likecomputing averages. to analyse the data. Mass data, which is collected, classified, tabulated andpresented systematically, is analysed further to bring its size to a single representative figure. This single

figure is the measure which can be found at central part of the range of all values. It is the one whichrepresents the entire data set. Hence, this is called the measure of central tendency.In other words, the tendency of data to cluster around a figure which is in central location is known ascentral tendency. Measure of central tendency or average of first order describes the concentration oflarge numbers around a particular value. It is a single value which represents all units.The two most common measures of central tendency are the median and the mean, which can beillustrated with an example. Suppose we draw a sample of five women and measure their weights. Theyweigh 100 pounds, 100 pounds, 130 pounds, 140 pounds, and 150 pounds.

Q5. Define population and sampling unit for selecting a random sample in each of the followingcases.

a) Hundred voters from a constituency

b) Twenty stocks of National Stock Exchangec) Fifty account holders of State Bank of Indiad) Twenty employees of Tata motors.

Answer:

Population: The totality of all units or individuals in a survey is called population or universe. If thenumber of objects in a population is finite then it is called finite population otherwise it is known as infinitepopulation.

The data that describes the characteristics of the population is known as parameter. In the figure below,the total number of eight consumers constitutes the entire population.Units: In a Statistical survey, the objects on which the characteristics are measured are called units orindividuals.

SampleA sample is a part or subset of the population. By studying the sample, you can predict the characteristicsof the entire population from where the sample is taken. The data that describes the characteristics of asample is known as statistic.

Q6. What is a confidence interval, and why it is useful? What is a confidence level?

Answer:

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In using interval estimates, we are not confined to 1,2 and 3 standard errors; for example, 1.64standard errors include about 90 percent of the area under the curve; it includes 0.4495 of the area oneither side of the mean in a normal distribution. Similarly, 2.58 standard error includes about 99 percentof the area, or 49.51 percent on either side of the mean. This probability indicates how confident we arethat the interval estimate will include the population parameter. A higher probability means moreonfidence. In estimation, the most commonly used confidence levels are 90 percent, 95 percent, and 99percent, but we are free to apply any confidence level.

In our book

ANS

1A) Pg No. (2-4)

B) 11-12

2a) 52

b) 25

c) 24

d)51

4) pg 74 and 113

6) 207