Unit 1 Statistics Class 11 Notes Cha 1 (Introduction To Statistics). MCQ Questions for Class 11 Economics with Answers were prepared based on the latest exam pattern.

## Introduction To Statistics

## Statistics Class 11 Notes Cha 1 (Introduction To Statistics)

**Q.1) Explain the difference between parameter and statistic.**

**Answer:****Parameter:**

A number that describes some property of a population is a parameter For example a numerical value such as mean and standard deviation calculated from population is known as parameter (i.e. u and 6 ), the population parameters are constants.**Statistic:**

A number that describes some property of a sample is called statistic. For example, the average height of all the students in the college is a parameter, where as the average length calculated for a random sample of such students from the college is a statistic. A numerical value such as mean and standard deviation calculated from sample is known as statistic. For example mean (x ) and standard deviation (s) are the statistic.

**Q.2) Define statistics. Distinguish between Descriptive and Inferential Statistics, giving suitable examples.**

**Answer:Statistics:**

Numerical data relating to an aggregate of individuals, the science of collecting, analyzing and interpreting data is called statistics.

**Descriptive statistics:**

Descriptive statistics comprises those methods concerned with collecting and describing a set of data so as to yield meaningful information. For example, a college teacher computes an average grade for his statistics class. The average grade describes the performance of that particular class but do not make a generalization about other classes, we can say that the college teacher is using descriptive statistics. The graphs, charts and other relevant computations in various newspapers and magazines usually fall in the area categorized as descriptive statistics.

**Inferential statistics:**

Inferential statistics comprises those methods concerned with the analyzing of a subset of data leading to inferences about the entire set of data.

For example the academic records of the matric classes during the past five years at a nearby Government school show that 45% of the entering freshmen eventually matriculated. The numerical value, 45%, is a descriptive statistic. If you are a member of the present freshmen class and conclude from this study that your chances of matriculating are better than 40%, you have made a statistical inference that is subject to uncertainty.

**Q.3) Explain the difference between population and a sample; use sketches for showing population, parameter and statistic.**

**Answer:**The aggregate, or totality, of all the individual items about which information is required.

Population is a statistical term, which is used to define a finite or infinite number of similar, or like. For example if 1000 students in the college that we classified according to blood type, we say that we have a population or universe of size 1000. Similarly, the heights of the students of Government College Lahore and children in a city are examples of populations.

It is very rare that we can examine all the objects in a population or have access to all the observations that can arise. More frequently we must be content with observing only a part of the population; such a part is called sampling.

**Population parameter:**

A numerical value such as mean and standard deviation calculated from population is known as parameter (i.e. u and 6 ), the population parameters are constants.

Consider, the example, the following set of data representing the number of typing errors made by a secretary on ten different pages of a document: 1, 2,1,2,1,1,4,0 and 2. For instance, we could make the statement that the largest number of typing errors on any single page was 4. We might state that the arithmetic mean of the ten numbers is 1.5 the numbers 4 and 1.5 are descriptive properties of our population we refer to such values as parameters of population. Note that a parameter u = 1.5 is a constant.

**Sample statistic:**

A numerical value such as mean and standard deviation calculated from sample is known as statistic. For example mean (x ) and standard deviation (s) are the sample statistic or simply a statistic. The value of the parameter is fixed whereas the value of statistic varies from sample to sample. Thus statistic is a random variable, which estimates the value of the parameter.

**Q.4) Discuss in detail the importance of Statistics in various disciplines.**

**Answer:**

t now widely used in Governments, industry and business. Its importance has now gone beyond science, engineering and technology and entered such areas as Law, Political Science and literature. Following are the importance of statistics in various disciplines.

1. Statistical data are now widely used in taking all administrative decisions:

· The authorities in Education Department are considering the question of opening new schools and colleges. Obviously, the decision will be based on knowledge of the school going population at different levels.

· The authorities want to revise the pay scales of employees in view of an increase in the cost of living. Statistical techniques may help to. Determine the rise in the cost of living.

2. Statistics plays an important role in business, because it provides a quantitative basis for arriving at decisions in all matters connected with operating of business. For example, a successful businessman must know the demand of his consumers. Statistics would help to plan production according to the demands of the consumers.

3. The banks make use of statistics while framing their policies. The banks have to conduct constant enquiries regularly deposits under different categories, the nature of demand for daily with-drawls etc. These information help them in forming “bank policies”. Hence the importance of the knowledge of statistics is indispensable to the banker.

4. The insurance companies decide the premium on the basis of data collected with regard to mortality rates at different ages.

5. Statistics has proved to be of immense use in Astronomy, Biology, Zoology, Physics, Chemistry, Agriculture, Meteorology, Economics, Psychology, Education and Sociology etc.

6. The tools of statistics are indispensable for transport authorities. The transport authorities before launching any new items first undertake a survey to see whether it would be feasible for them or not. The information collected through the survey from the basis for new scheme in nature’ and the transport authorities are with the passage of time the importance of statistics becomes wider and wider. The science of statistics has grown to the extent that there is hardly any field in which its need is not felt. Thus statistics now- holds a central position in almost every field and its importance cannot be defined.

**Q.5) Why is a course in Statistics important to you as a student?**

**Answer:**

Biology, physics, chemistry, meteorology, sociology, communication, and even information technology all use statistics. For many of these categories, the use of statistics in that field involves collecting data, analyzing it, coming up with a hypothesis, and testing that hypothesis.

In biology, the use of statistics within that field is known as biostatistics, biometry, or biometrics. Biostatistics often involves the design of experiments in medicine, online pharmacy agriculture, and fishery. It also involves collecting, summarizing, and analyzing the data received from those experiments as well as the decided results. Medical biostatistics is a separate branch that deals mainly with medicine and health. Learn biology with an online course.

Physics uses probability theory and statistics dealing mainly with the estimation of large populations. In fact, the phenomenological results of thermodynamics were developed using the mechanics of statistics. Learn quantum physics with this course.

There are further examples of statistics in these sciences fields including analytical chemistry, which involves the presentation of problems in data analysis and demonstrating steps to solve them. Meteorology uses statistics in stochastic-dynamic prediction, weather forecasting, probability forecasting, and a number of other fields.

Sociology uses statistics to describe, explain, and predict from data received. Like many of the sciences, communication uses statistical methods to communicate data received. Information technology also uses statistics to predict particular outcomes.

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**Q.6) Define sampling distribution with sketches.**

**Answer:Sampling distributions:**

Consider all possible samples of size n, which can be drawn from a given population with replacement or without replacement. For each sample we can compute a statistic such as the mean x and standard deviation (s) etc. In this manner we obtain a distribution of statistic, which is called its sampling distribution. For example, if the particular statistic used in the sample means, the distribution is called the sampling distribution or sampling distribution of means.

**Sketches of sampling distribution**of means from the population 2, 4 and 4. Considering all possible sample of size 2, which can be drawn with replacement, Here N = population size = 3 and n = sample size = 2,

Total possible samples = N

^{n}= 3

^{2 }= 9

**Q.7) Define Statistics and explain how it can help in the establishment of sound business and banking.**

**Answer:**

Statistics is the science which deals with the collection analysis and Interpretation of numerical data”. Statistics plays an important role in business, because it provides a quantitative basis for arriving at decisions in all matters connected with operating of business. For example, a successful businessman must know the demand of his consumers. Statistics would help to plan production according to the demands of the consumers.

The banks make use of statistics while framing their policies. The banks have to conduct constant enquiries regularly deposits under different categories, the nature of demand for daily etc. This information helps them in forming “bank policies”.

Hence the importance of the knowledge of statistics is indispensable to the bankers.

**Q.8) How far is it correct to say, “Planning without Statistics is not possible”? Discuss.**

**Answer:**

Today we live in a period of transition, economic activities are being more and more closely directed to the production of such goods, and the provision of such goods, as the Government may decide to be most urgently required. If we study the economic plans implemented in various countries in recent times we will find that all of them are a statistical study of the economic resources of the respective countries, and they suggest possible ways and means of utilizing these resources in the best possible manner.

Planning without Statistics is not possible because statistics is used in economic planning for following purposes.

1.It becomes possible to compare the development of one country with the other, with the help of statistical figures.

2. The information about progress in production, capital formation etc are involved through the figures supplied by statistical inquiries.

3. The relative importance of consumption, production, exchange can be known from the data, supplied by statistical surveys.

4. Priorities are determined and targets are fixed, in the planning. This is possible only when relevant data is available.

5. Plans are evaluated on the bases of data collected in this context.

**Q.9) What is a variable? Distinguish between discrete and continuous variables, giving appropriate examples.**

**Answer:**

A quantity, which may take any one of a specified set of values or a characteristic that can take on different possible values, is called a variable.

For example, height of students, rainfall at a place price of a commodity etc. Variables may be of quantitative and qualitative nature.**Discrete variable**:

A discrete variable can assume only a finite number of values between any two points, e.g. the number of children in a family, the number of goals scored by a player, the number of deaths in an accident, etc.**Continuous variable:**A continuous variable may take an infinite number of values between any two points such as the height of a student, the temperature, at a place, the distance covered by a tourist etc.

**Q.10) **State which of the following represent discrete and which represent continuous variables and why?

i) The number of children in a family.

ii) The height of an individual.

iii) The number of fatal car accidents in a city in a given year.

iv) The income in a year for a family.

v) The number of claims on an insurance policy in a particular year.

vi) The number of errors detached in a company’s accounts.

vii) The amount of oil imported into Pakistan in a particular month.

viii) The percentage of impurity in a batch of chemicals.

ix) Lengths of 500 parts produced by a machine.

**Answer:**

· The number of children in a family. (D)

· The height of an individual. (C)

· The number of fatal car accidents in a city in a given year. (D)

· The income in a year for a family. (D)

· The number of claims on an insurance policy in a particular Year. (D)

· The number of errors detached in a company’s accounts. (D)

· The amount of oil imported into Pakistan in a particular Month. (D)

· The percentage of impurity in a batch of chemicals. (D)

· Lengths of 500 parts produced by a machine. (D)

### Q.11) Distinguish between quantitative and qualitative variables.

Pick out quantitative and qualitative variables.

i) The number of literate males.

ii) The number of unemployed people.

iii) The heights of fathers.

iv) The income in rupees.

v) The number of girls with blue eyes.

**Answer:**

Variables may be of quantitative and qualitative nature. If the values are expressed numerically the variable is said to be quantitative, such as age, weights, income, or number of children. On the other hand if the values refer to non-numerical qualities, the variable is said to be qualitative such as sex, poverty, eye color smoking, and intelligence. The variables are denoted by capital letters such that X, Y or Z, while small letters x, y or z denotes their values.

A quantitative variable may be classified as discrete or continuous variable.

(i) Quantitative

(ii) Quantitative

(iii) Quantitative

(iv) Quantitative

(v) Qualitative

**Q.12) Explain different sources of data.**

**Answer:**

Statistics is not only concerned with organizing and analyzing data once they are assembled, but also with the sources of data and how data are collected for study. As far as the national statistics are concerned the main sources are the Statistics Division and the Bureau of statistics of each province. Statistical year Books, monthly statistical bulletins, and several other publications.

The census organization publishes census reports containing information about all-important characteristics of population. The planning Division brings out Economic survey at the end of each year, which provides information regarding economic activities. The Ministry of Agriculture can find the data on agriculture from the Agriculture year Book published. State Bank bulletins supply unto data information regarding financial statistics. Other organizations like; corporations, banks, industries, etc. publish annual reports that contain summaries of their financial, social and producing activities.