Monsieur oreille is the husband of oreille madame. ਮੌਨਸੀਅਰ ਓਰੇਲੀ ਓਰੀਲੀ ਮੈਡਮ ਦਾ ਪਤੀ ਹੈ।
He looks like a gentle, weak and self-respecting man. ਉਹ ਇੱਕ ਕੋਮਲ, ਕਮਜ਼ੋਰ ਅਤੇ ਸਵੈ-ਮਾਣ ਵਾਲਾ ਆਦਮੀ ਜਾਪਦਾ ਹੈ।
His wife always is dominated him. ਉਸ ਦੀ ਪਤਨੀ ਹਮੇਸ਼ਾ ਉਸ ਉੱਤੇ ਹਾਵੀ ਹੁੰਦੀ ਹੈ.
He has to obey her all domestic affairs. ਉਸ ਨੂੰ ਸਾਰੇ ਘਰੇਲੂ ਮਾਮਲਿਆਂ ਦੀ ਪਾਲਣਾ ਕਰਨੀ ਪੈਂਦੀ ਹੈ।
He belongs to a rich family. ਉਹ ਇੱਕ ਅਮੀਰ ਪਰਿਵਾਰ ਨਾਲ ਸਬੰਧ ਰੱਖਦਾ ਹੈ। character sketch of Monsieur Oreille
So he does not need to work for a living. ਇਸ ਲਈ ਉਸ ਨੂੰ ਰੋਜ਼ੀ-ਰੋਟੀ ਲਈ ਕੰਮ ਕਰਨ ਦੀ ਲੋੜ ਨਹੀਂ ਹੈ।
But his wife wants him to earn more. ਪਰ ਉਸਦੀ ਪਤਨੀ ਚਾਹੁੰਦੀ ਹੈ ਕਿ ਉਹ ਹੋਰ ਕਮਾਵੇ।
They have no children and other financial responsibilities. ਉਨ੍ਹਾਂ ਦੇ ਕੋਈ ਬੱਚੇ ਨਹੀਂ ਹਨ ਅਤੇ ਹੋਰ ਵਿੱਤੀ ਜ਼ਿੰਮੇਵਾਰੀਆਂ ਹਨ।
He works in the War Office as a head clerk. ਉਹ ਵਾਰ ਦਫ਼ਤਰ ਵਿੱਚ ਹੈੱਡ ਕਲਰਕ ਵਜੋਂ ਕੰਮ ਕਰਦਾ ਹੈ।
He is not a rational person in the eyes of his wife. ਉਹ ਆਪਣੀ ਪਤਨੀ ਦੀਆਂ ਨਜ਼ਰਾਂ ਵਿਚ ਤਰਕਸ਼ੀਲ ਵਿਅਕਤੀ ਨਹੀਂ ਹੈ।
His wife is a stingy woman. ਉਸਦੀ ਪਤਨੀ ਇੱਕ ਕੰਜੂਸ ਔਰਤ ਹੈ।
She wants to save every coin and does not want to spend even on essential affairs. ਉਹ ਹਰ ਸਿੱਕਾ ਬਚਾਉਣਾ ਚਾਹੁੰਦੀ ਹੈ ਅਤੇ ਜ਼ਰੂਰੀ ਕੰਮਾਂ ‘ਤੇ ਵੀ ਖਰਚ ਨਹੀਂ ਕਰਨਾ ਚਾਹੁੰਦੀ।
She also wants about his husband to have a better standard of living. ਉਹ ਇਹ ਵੀ ਚਾਹੁੰਦੀ ਹੈ ਕਿ ਉਸਦੇ ਪਤੀ ਦਾ ਜੀਵਨ ਪੱਧਰ ਬਿਹਤਰ ਹੋਵੇ।
His sleep fled at nights when he would like to spend money on anything. ਰਾਤਾਂ ਨੂੰ ਉਸਦੀ ਨੀਂਦ ਉੱਡ ਜਾਂਦੀ ਸੀ ਜਦੋਂ ਉਹ ਕਿਸੇ ਵੀ ਚੀਜ਼ ‘ਤੇ ਪੈਸਾ ਖਰਚ ਕਰਨਾ ਚਾਹੁੰਦਾ ਸੀ।
He considered his pairing with the wrong woman. ਉਹ ਗਲਤ ਔਰਤ ਨਾਲ ਆਪਣੀ ਜੋੜੀ ਸਮਝਦਾ ਸੀ।
He had to go to the office with an old umbrella. ਉਸ ਨੇ ਪੁਰਾਣੀ ਛੱਤਰੀ ਲੈ ਕੇ ਦਫ਼ਤਰ ਜਾਣਾ ਸੀ। character sketch of Monsieur Oreille
His colleagues laugh at his umbrella. ਉਸਦੇ ਸਾਥੀ ਉਸਦੀ ਛੱਤਰੀ ‘ਤੇ ਹੱਸਦੇ ਹਨ। character sketch of Monsieur Oreille
Then his wife buys a new cheap umbrella for his husband. ਫਿਰ ਉਸਦੀ ਪਤਨੀ ਉਸਦੇ ਪਤੀ ਲਈ ਇੱਕ ਨਵੀਂ ਸਸਤੀ ਛੱਤਰੀ ਖਰੀਦਦੀ ਹੈ।
But this umbrella is considered as an advertising purpose. ਪਰ ਇਸ ਛਤਰੀ ਨੂੰ ਇਸ਼ਤਿਹਾਰਬਾਜ਼ੀ ਦਾ ਮਕਸਦ ਮੰਨਿਆ ਜਾਂਦਾ ਹੈ।
Then she buys for him a costly umbrella. ਫਿਰ ਉਹ ਉਸ ਲਈ ਮਹਿੰਗੀ ਛੱਤਰੀ ਖਰੀਦਦੀ ਹੈ।
But this umbrella gets burnt in the office. ਪਰ ਦਫ਼ਤਰ ਵਿੱਚ ਇਹ ਛੱਤਰੀ ਸੜ ਜਾਂਦੀ ਹੈ। character sketch of Monsieur Oreille
Then his wife abuses him. ਫਿਰ ਉਸਦੀ ਪਤਨੀ ਉਸਨੂੰ ਗਾਲ੍ਹਾਂ ਕੱਢਦੀ ਹੈ।
But as we know, he is an innocent man. ਪਰ ਜਿਵੇਂ ਕਿ ਅਸੀਂ ਜਾਣਦੇ ਹਾਂ, ਉਹ ਇੱਕ ਬੇਕਸੂਰ ਆਦਮੀ ਹੈ।
But for all such his stingy wife is responsible for his ridiculous position in the office. ਪਰ ਅਜਿਹੇ ਸਭ ਲਈ ਉਸਦੀ ਕੰਜੂਸ ਪਤਨੀ ਦਫਤਰ ਵਿੱਚ ਉਸਦੀ ਹਾਸੋਹੀਣੀ ਸਥਿਤੀ ਲਈ ਜ਼ਿੰਮੇਵਾਰ ਹੈ।
He is a self respecting man. ਉਹ ਇੱਕ ਸਵੈ-ਮਾਣ ਵਾਲਾ ਆਦਮੀ ਹੈ।
He tells his wife that he would not go to the office with a servant’s umbrella. ਉਹ ਆਪਣੀ ਪਤਨੀ ਨੂੰ ਕਹਿੰਦਾ ਹੈ ਕਿ ਉਹ ਨੌਕਰ ਦੀ ਛੱਤਰੀ ਲੈ ਕੇ ਦਫ਼ਤਰ ਨਹੀਂ ਜਾਵੇਗਾ।
Even though he threatens his wife to resign from his job. ਭਾਵੇਂ ਉਹ ਆਪਣੀ ਪਤਨੀ ਨੂੰ ਨੌਕਰੀ ਤੋਂ ਅਸਤੀਫਾ ਦੇਣ ਦੀ ਧਮਕੀ ਦਿੰਦਾ ਹੈ।
He is a character of pity in this story. ਉਹ ਇਸ ਕਹਾਣੀ ਵਿਚ ਤਰਸ ਦਾ ਪਾਤਰ ਹੈ।
It is a really painful sight for such a good man. ਅਜਿਹੇ ਨੇਕ ਆਦਮੀ ਲਈ ਇਹ ਬਹੁਤ ਦਰਦਨਾਕ ਦ੍ਰਿਸ਼ ਹੈ।
He is being ill-treated by his miserly wife. ਉਹ ਆਪਣੀ ਕੰਜੂਸ ਪਤਨੀ ਦੁਆਰਾ ਬੁਰਾ ਸਲੂਕ ਕੀਤਾ ਜਾ ਰਿਹਾ ਹੈ।
character sketch of Monsieur Oreille
character sketch of Monsieur Oreille
You can get information about your syllabus from the gndu for the purpose of reading this character sketch.
This punjabi poem describes nature sorrow which is given by human being while a person tells it his grief in his life. But nature also console him that don’t afraid to living his life on earth.
This punjabi poem maa da pyar tells us what does our mother for us in her whole life. So, we must not forget her virtue for us in our life. Thus, we must pay thanks to her feet.
Thus, this poem describes the freedom of butterfly. Which has freedom to wandered anywhere. Whereas as like the human being no need it passport ID.
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Q.6 (a) Define the term ‘Hypothesis’. Explain in detail the procedure of testing a Hypothesis. ( Mcom-l 2024 )
Meaning / Definition of Hypothesis
A hypothesis is a tentative statement or assumption about a population parameter which we want to test on the basis of sample information.
It is a logical guess about the value of a population mean, proportion, difference of means, etc., framed in a way that it can be tested statistically. procedure of testing a Hypothesis.
Example: “The average monthly income of teachers is ₹40,000” is a hypothesis about population mean.
Procedure / Steps of Testing a Hypothesis
Formulation of hypotheses
First of all two hypotheses are framed:
(i) Null hypothesis (H₀) – It is a statement of no difference / no effect / no change.
Example: H₀ : μ = 40,000 (average income is ₹40,000).
(ii) Alternative hypothesis (H₁ or Hₐ) – It is a statement that contradicts H₀ and represents what we want to prove.
Example: H₁ : μ ≠ 40,000 (average income is not ₹40,000).
Selection of level of significance (α)
Decide the maximum probability of rejecting a true H₀ which the researcher is willing to take.
Common levels: 5% (0.05) or 1% (0.01).
Smaller α means stricter test and lesser chance of Type I error. procedure of testing a Hypothesis.
Selection of an appropriate test statistic
According to the nature of the problem, size of sample and type of data, choose a suitable test:
Z-test, t-test, chi-square test, F-test, etc.
Define the test statistic formula, e.g.
for testing a population mean when σ is known. procedure of testing a Hypothesis.
Determination of sampling distribution and critical region
Identify the sampling distribution of the test statistic under H₀ (normal, t, chi-square, F).
For the chosen α, obtain the critical value(s) from statistical tables.
Decide whether the test is:
Two-tailed (H₁: parameter ≠ hypothesised value), or
Left-tailed (H₁: parameter < value), or
Right-tailed (H₁: parameter > value).
The critical region (rejection region) consists of those values of the test statistic for which H₀ will be rejected. procedure of testing a Hypothesis.
Collection of sample data and computation of test statistic
Draw a random sample from the population.
Using sample observations, calculate the value of the test statistic (Z, t, χ², F etc.) according to the selected formula.
Decision regarding H₀
Compare the calculated value of the test statistic with the tabulated (critical) value:
If the calculated value falls in the critical region, reject H₀.
If the calculated value falls in the acceptance region, do not reject H₀ (i.e., H₀ is accepted at the chosen level of significance).
Conclusion / Interpretation
Express the statistical decision in simple words relating to the problem. procedure of testing a Hypothesis.
Example: “At 5% level of significance, the hypothesis that the average monthly income of teachers is ₹40,000 is rejected; therefore, the average income is significantly different from ₹40,000.”
Q.6 (b) Differentiate Null and Alternative Hypothesis giving examples.
1. Meaning
Null Hypothesis (H₀):
A statement that there is no difference, no effect, or no relationship in the population. It is the hypothesis to be tested and is assumed to be true unless evidence suggests otherwise.
Alternative Hypothesis (H₁ / Hₐ):
A statement that contradicts H₀. It expresses the presence of a difference, effect or relationship and represents what the researcher aims to support.
2. Nature of statement
H₀ usually includes equality sign (=, ≤, ≥).
H₁ includes inequality sign (≠, >, <).
3. Role in testing
H₀ is the basis of the testing procedure; all calculations (sampling distribution, standard error, etc.) are made on the assumption that H₀ is true. procedure of testing a Hypothesis.
H₁ is accepted only when H₀ is rejected. It is supported by the sample evidence.
4. Attitude of researcher
H₀: The researcher tries to find whether there is sufficient evidence against it.
H₁: The researcher actually wishes to prove or support this hypothesis.
5. Symbol
Null hypothesis is denoted by H₀.
Alternative hypothesis is denoted by H₁ or Hₐ. procedure of testing a Hypothesis.
6. Example (two-tailed test)
Suppose a company claims that the mean life of its bulbs is 1,000 hours. A researcher wants to test this claim.
H₀: μ = 1,000 hours (mean life is 1,000 hours).
H₁: μ ≠ 1,000 hours (mean life is not 1,000 hours).
Example (right-tailed test)
A new teaching method is believed to increase the average marks of students beyond 60.
H₀: μ ≤ 60
H₁: μ > 60
Example (left-tailed test)
A machine is supposed to fill bottles with at least 500 ml of liquid. procedure of testing a Hypothesis.
H₀: μ ≥ 500 ml
H₁: μ < 500 ml
In every case, we first assume H₀ is true, perform the test, and then decide whether to reject H₀ and accept H₁, or to continue to accept H₀ at the chosen level of significance.
If you would like to know the Syllabus of Statistical Analysis For Business of M.Com-l of Gndu. You must visit the official website of Gndu.
👉 Important questions of Statistical Analysis For Business
Q.5 Explain Questionnaire. Explain the steps involved in constructing a questionnaire.
Meaning of Questionnaire
A questionnaire is a list or schedule of questions prepared by the researcher for collecting information from respondents.
It is usually a printed or typed set of questions arranged in a proper order. The respondents read the questions, record their answers in the given space and return the questionnaire to the investigator. It is widely used in surveys, opinion studies and market research.
Characteristics / Features of a Good Questionnaire
It is related to a specific problem or objective of the study.
Questions are simple, clear and easily understood.
Questions are arranged in a logical sequence.
It avoids personal, embarrassing and leading questions.
It is neither too long nor too short.
Adequate space is provided for answers. steps involved in constructing a questionnaire
It contains necessary instructions to help the respondent in answering.
Steps involved in Constructing a Questionnaire
Defining the Objectives of the Study
First of all, the researcher must be clear about the purpose of the enquiry – what information is required and why it is required.
Clear objectives help in selecting relevant questions and avoiding unnecessary ones.
Deciding the Information to be Collected
The researcher then decides what specific data are needed to achieve the objectives.
For example: personal details, income, education, preferences, opinions, etc. steps involved in constructing a questionnaire
Only useful and relevant items should be included.
Identifying the Respondents and Mode of Contact
The target group of respondents (students, customers, employees, etc.) and the way of contacting them (by post, online, personal interview) should be decided. steps involved in constructing a questionnaire
This affects the language, length and layout of the questionnaire.
Deciding the Types of Questions
The researcher chooses suitable form of questions, such as:
(a) Closed-ended questions – answers are limited to given alternatives like Yes/No, Agree/Disagree, multiple choice, rating scale, etc.
(b) Open-ended questions – respondents are free to write their own answers. steps involved in constructing a questionnaire
A good questionnaire usually combines both types depending on the information required.
Drafting the Questions (Wording of Questions)
Questions should be written in simple, clear and polite language.
Technical terms, double-meaning words and long sentences should be avoided.
Questions should not be leading or biased, and should not hurt the feelings of the respondent.
Only one idea should be asked in one question. steps involved in constructing a questionnaire
Deciding the Sequence or Order of Questions
Begin with simple, general and interesting questions to create interest and gain cooperation.
More complex, detailed and personal questions should be placed in the middle.
Classification questions like age, sex, income, etc. may be kept at the end. steps involved in constructing a questionnaire
The order should be logical so that the respondent can move smoothly from one question to another.
Design and Layout of the Questionnaire
The questionnaire should have an attractive and neat appearance. steps involved in constructing a questionnaire
A suitable title and number of the questionnaire should be given.
Clear instructions should be printed about how to answer, how to mark a choice, and how to return the form.
Adequate space should be left for answers, especially for open-ended questions.
Pages should be numbered and questions may also be numbered for easy reference.
Preparation of Introductory Note / Covering Letter
A brief introduction is given at the beginning explaining:
who is conducting the survey,
the purpose of the study,
assurance of confidentiality of answers, and
thanks for cooperation.
This increases the response rate and builds trust.
Pre-testing / Pilot Study
Before using the questionnaire on a large scale, it should be tried on a small group of respondents similar to the actual sample. steps involved in constructing a questionnaire
This pilot test helps in finding out ambiguous questions, unnecessary items, difficulties in understanding, length of time taken, etc.
Revision and Finalization
On the basis of feedback from the pilot study, necessary changes are made.
Confusing or irrelevant questions are modified or removed. steps involved in constructing a questionnaire
The final questionnaire is then printed or prepared for distribution.
Coding Plan and Numbering
For easy analysis of data, possible answers of closed questions may be given code numbers in advance.
Questions and response categories are systematically numbered to facilitate tabulation and computer entry later.
Conclusion
A questionnaire is a very important tool of data collection in surveys. A well-constructed questionnaire saves time and cost, gives accurate and comparable information and increases the reliability of the research. Therefore, the researcher must follow systematic steps – from defining objectives to pilot testing and finalizing – to ensure that the questionnaire is clear, relevant and capable of giving the required data.
If you would like to know the Syllabus of Statistical Analysis for business M.com-l of Gndu, you must visit the official website of Gndu.
👉 important questions of Statistical Analysis For Business
Primary data are those data which are collected for the first time, directly from the original source by the investigator for a specific purpose of his/her own study.
They are also called first–hand data or original data.
Features / Characteristics
Originality – They are collected afresh, directly from respondents or situations.
Specific Purpose – They are collected keeping in view a particular problem or objective of the investigation.
Greater Accuracy and Reliability – As they are collected by proper methods and under the control of the investigator, they are usually more accurate.
Time-consuming and Costly – Collection of primary data needs more time, more money and more manpower.
First Stage in Statistical Inquiry – Every statistical investigation begins with collection of primary data; later, these may become secondary data for some other investigation.
2. Sources / Methods of Collecting Primary Data
Primary data can be collected from various sources and with different methods. Important methods are:
Direct Personal Investigation
The investigator himself goes to the field and contacts the respondents personally. Differentiate between Primary and Secondary Data.
He asks questions, observes the facts and records the answers on the spot.
Suitable when the area of enquiry is small and information required is of confidential nature.
Indirect Oral Investigation
The investigator does not contact the persons about whom the information is needed, but contacts witnesses or experts who are expected to know about them. Differentiate between Primary and Secondary Data.
Commonly used in estimating income, expenditure, credit-worthiness etc.
Information from Local Agents / Correspondents
The investigator appoints local agents or correspondents in different areas.
These agents collect information regularly and send it to the central office.
Newspapers and market-research agencies often use this method. Differentiate between Primary and Secondary Data.
Mailed Questionnaire Method
A list of well-framed questions (questionnaire) is prepared and sent by post or e-mail to the selected respondents.
Respondents read the questions and record their answers in the space provided and send them back. Differentiate between Primary and Secondary Data.
Useful when the investigation covers a wide area and respondents are educated.
Schedules through Enumerators
Instead of sending a questionnaire, trained enumerators visit the respondents, ask questions and fill the schedules themselves.
Very useful when respondents are illiterate or the questions are complicated.
Personal Interview / Telephone / Online Interview
Information is obtained by face-to-face or telephone or video interview.
The interviewer asks questions and records answers immediately.
Useful for opinion surveys, market surveys etc. Differentiate between Primary and Secondary Data.
Observation Method
Data are collected by directly observing the behaviour of persons, objects or events, e.g. counting vehicles passing through a road, studying buying behaviour of customers in a shop etc.
Helpful when respondents may not give correct answers.
Experimental Method
Data are obtained by conducting controlled experiments, e.g. testing a new variety of seed, new medicine, or new advertisement. Differentiate between Primary and Secondary Data.
Very useful in physical sciences and also in social sciences.
3. Difference between Primary Data and Secondary Data
Secondary data are those which have already been collected and processed by someone else for some other purpose and are being used by the investigator for his present study.
Important points of distinction:
Origin
Primary data: Collected first-hand by the investigator himself.
Secondary data: Already collected by some other person or organisation.
Purpose of Collection
Primary: Collected with a specific objective of the present enquiry.
Secondary: Collected earlier for some other purpose; present use is only a by-product. Differentiate between Primary and Secondary Data.
Originality and Accuracy
Primary: More original and usually more accurate because the investigator controls the method of collection.
Secondary: May be less accurate; reliability depends on the competence and object of the original collector.
Cost
Primary: Collection is expensive – needs more money, time and staff.
Secondary: Comparatively cheap, because data are already available. Differentiate between Primary and Secondary Data.
Time Required
Primary: Time-consuming; many stages like planning, collection, scrutiny etc.
Secondary: Time-saving; data can be obtained quickly from published or unpublished sources.
Suitability
Primary: Highly suitable to the present study, as they are collected keeping in view the specific requirements.
Secondary: May not be fully suitable; they may relate to different units, definitions or time periods. Differentiate between Primary and Secondary Data.
Dependence
Primary: Investigator is independent; he decides the coverage, accuracy and method.
Secondary: Investigator is dependent on others for the quality, coverage and method of collection.
Form of Presentation
Primary: Generally in raw form and need classification and tabulation by the investigator.
Secondary: Often already classified, tabulated and sometimes analysed.
Use in Research
Primary: Used when fresh and detailed information is required.
Secondary: Used for preliminary study, comparison, or when primary data collection is not possible. Differentiate between Primary and Secondary Data.
Conclusion:
Primary data are first-hand, original and highly suitable for a specific investigation but are costly and time-consuming to collect. Secondary data are already available, cheaper and quicker to use but may not fully meet the exact needs of the present study and may suffer from limitations of accuracy and suitability.
If you would like to know the Syllabus of Statistical Analysis For Business of M.Com-l of Gndu, You must visit the official website of Gndu.
👉 Important questions of Statistical Analysis for Business
3. What do you understand by Sampling? Elaborate various methods of Probability and Non-Probability Sampling.
Answer:
Meaning of Sampling
Sampling is a statistical technique in which only a small part (sample) of the entire population is selected for study, instead of studying the whole population. This sample is carefully chosen so that the information collected from it represents the entire population accurately.
Sampling helps in saving time, cost, and effort, and also makes data collection more practical and feasible.
Sampling methods are broadly classified into two categories:
Probability Sampling
Non-Probability Sampling
1. Probability Sampling Methods
In probability sampling, every unit of the population has a known and equal chance of being selected. This method gives more accurate and unbiased results. Methods of Sampling probability
(a) Simple Random Sampling
Each individual of the population has an equal chance of being chosen. Selection is done randomly using methods like lottery or random number tables.
(b) Systematic Sampling
Here, the first unit is selected randomly, and the next units are selected at regular intervals.
Example: Selecting every 10th person from a list.
(c) Stratified Sampling
The population is divided into different groups called strata (such as age, income, gender). From each strata, samples are selected randomly.
This ensures representation of all important groups. Methods of Sampling probability
(d) Cluster Sampling
The population is divided into clusters (groups) like districts, villages, or schools. Some clusters are selected randomly and all or some units from those clusters are studied.
(e) Multistage Sampling
Sampling is done in different stages.
Example: Select districts → then villages → then households. Methods of Sampling probability
2. Non-Probability Sampling Methods
In this method, every unit does NOT have an equal chance of being selected. Selection depends on the judgement or convenience of the researcher. It is less reliable but easier to conduct.
(a) Convenience Sampling
The sample is selected from individuals who are easily available.
Example: Surveying students in a nearby college. Methods of Sampling probability
(b) Judgement or Purposive Sampling
The researcher selects the sample based on their own judgement about who will give the best information.
Example: Selecting expert doctors for a health survey.
(c) Quota Sampling
The population is divided into groups (like male/female), and a fixed number (quota) is selected from each group based on convenience. Methods of Sampling probability
(d) Snowball Sampling
Used when the population is difficult to identify. Existing respondents help in identifying more respondents.
Example: Survey among drug addicts or rare disease patients.
Conclusion
Sampling is an essential tool in statistics that helps in collecting accurate information in a cost-effective and time-efficient manner. Probability sampling is more scientific and unbiased, while non-probability sampling is easier but less reliable. Methods of Sampling probability
If you would like to know the Syllabus of Statistical Analysis for business, you must visit the official website of Gndu.
👉 Important questions of Statistical Analysis For Business of M.Com-l of Gndu.
The average test marks in a particular class is 79.
The average test marks in a particular class is 79. The standard deviation is 5. Marks are normally distributed. We have to find how many students, in a class of 200, did not receive marks between 75 and 82.
Given: Mean (μ) = 79 Standard deviation (σ) = 5 Class size = 200 Given probabilities (for standard normal variable Z): P(0 ≤ Z ≤ 0.7) = 0.2580 P(0 ≤ Z ≤ 0.8) = 0.2880 P(0 ≤ Z ≤ 0.6) = 0.2257
Step 1: Convert the raw scores to Z-scores.
For X = 75: Z1 = (75 − 79) / 5 Z1 = −4 / 5 Z1 = −0.8
For X = 82: Z2 = (82 − 79) / 5 Z2 = 3 / 5 Z2 = 0.6
So, we want the probability that marks are not between 75 and 82, i.e. P(X < 75 or X > 82). First we will find P(75 ≤ X ≤ 82), then subtract from 1.
Step 2: Find P(75 ≤ X ≤ 79) and P(79 ≤ X ≤ 82).
Because the normal distribution is symmetric about the mean:
P(75 ≤ X ≤ 79) = P(−0.8 ≤ Z ≤ 0) = P(0 ≤ Z ≤ 0.8) From the given values: P(0 ≤ Z ≤ 0.8) = 0.2880
P(79 ≤ X ≤ 82) = P(0 ≤ Z ≤ 0.6) From the given values: P(0 ≤ Z ≤ 0.6) = 0.2257
Step 3: Probability of marks lying between 75 and 82.
P(75 ≤ X ≤ 82) = P(75 ≤ X ≤ 79) + P(79 ≤ X ≤ 82) P(75 ≤ X ≤ 82) = 0.2880 + 0.2257 P(75 ≤ X ≤ 82) = 0.5137
Step 4: Probability of marks lying outside 75 and 82.
P(X < 75 or X > 82) = 1 − P(75 ≤ X ≤ 82) P(X < 75 or X > 82) = 1 − 0.5137 P(X < 75 or X > 82) = 0.4863
Step 5: Convert probability into number of students.
Number of students not getting marks between 75 and 82 = 0.4863 × 200 = 97.26 ≈ 97 students
Final Answer: Approximately 97 students in the class of 200 did not receive marks between 75 and 82.
A random variable is a variable whose value is determined by chance.
Example:
Number of heads in 3 coin tosses
Marks obtained by a student
Height of a person
(2) What is Probability Distribution?
A probability distribution is a systematic description of how the probabilities are assigned to different possible values of a random variable.
It tells us:
Which values the variable can take
How likely (what probability) each value is
So, in simple words:
Probability distribution = a rule / function that shows the pattern of probabilities for all possible outcomes of a random variable.
(3) Types of Probability Distribution
(a) Discrete Probability Distribution
Random variables take finite or countable values (0, 1, 2, 3, …).
Probabilities are assigned to each distinct value.
Examples:
Binomial distribution
Poisson distribution
Example in simple numbers:
Toss one fair coin
P(Head) = 0.5
P(Tail) = 0.5
This is a discrete probability distribution.
(b) Continuous Probability Distribution
Random variables can take any value in an interval (infinitely many values).
We do not talk about probability at a point, but probability over an interval.
Examples:
Normal distribution
Exponential distribution
t-distribution
(4) Example to Understand
Consider the heights of students in a class.
Everyone’s height is slightly different
Values are not countable like 1, 2, 3 – they are continuous (e.g., 165.2 cm, 165.8 cm, etc.)
Their distribution usually forms a bell-shaped curve → this is a normal distribution, which is a type of continuous probability distribution.
2. Normal Distribution – Meaning
(1) Definition
The Normal Distribution is a continuous probability distribution that is:
Bell-shaped
Symmetrical
Unimodal (one peak)
It is also called the Gaussian distribution.
(2) Parameters
A normal distribution is completely determined by two parameters:
Mean (μ) → central location
Standard deviation (σ) → spread or dispersion
Different values of μ and σ change the position and shape of the curve.
3. Characteristics of Normal Distribution (Step-wise)
(1) Bell-shaped Curve
The graph of a normal distribution is bell-shaped.
Most observations are around the center, fewer in the tails.
(2) Symmetry about the Mean
The curve is perfectly symmetrical about the mean (μ). What is Probability Distribution
The left half is a mirror image of the right half.
Therefore:
Mean = Median = Mode
(3) Mean and Standard Deviation Decide Shape
Mean (μ): fixes the centre of the curve.
Standard deviation (σ): fixes the spread of the curve. What is Probability Distribution
Large σ → curve is wider and flatter
Small σ → curve is narrower and sharper (more peaked)
(4) Total Area Under the Curve = 1
The normal curve is a probability density function.
The total area under the curve (from −∞ to +∞) is equal to 1, meaning total probability = 1.
Probability of a range of values = area under the curve over that range.
(5) Asymptotic to X-axis
The two tails of the curve extend indefinitely in both directions (towards −∞ and +∞).
They approach the X-axis but never touch it.
This means extreme values are possible but have very small probabilities.
(6) Unimodal
The curve has only one peak (one mode).
Maximum frequency occurs at the mean.
(7) Empirical Rule (68%–95%–99.7% Rule)
In a normal distribution:
About 68% of observations lie within ±1σ of the mean (μ − σ to μ + σ)
About 95% lie within ±2σ of the mean (μ − 2σ to μ + 2σ)
About 99.7% lie within ±3σ of the mean (μ − 3σ to μ + 3σ)
This is very useful in practice to understand how data is spread around the mean. What is Probability Distribution
(8) Mathematical Form
The probability density function (PDF) of the normal distribution is:
f(x) = 1 (2-μ)2 202 σν2π
You don’t always need to derive it in exams, but you should know that:
It depends on μ and σ
It ensures total area = 1
(9) Standard Normal Distribution
If we convert any normal variable X to:
Z = \frac{X – \mu}{\sigma}
Mean = 0
Standard deviation = 1
For this, Z-tables are used to find probabilities.
4. Applications of Normal Distribution (Step-wise)
Normal distribution is extremely important in statistics and real life.
(1) Natural and Biological Measurements
Many natural phenomena are approximately normally distributed, such as:
Heights and weights of people
Blood pressure, pulse rate
Scores in intelligence (IQ) tests
Measurement errors in experiments
Because of this, normal distribution is often called a “natural law of errors”. What is Probability Distribution
(2) Basis of Statistical Inference
Normal distribution plays a central role in:
(a) Estimation
Used in constructing confidence intervals for means and proportions.
(b) Hypothesis Testing
Many tests (Z-test, t-test approximations, etc.) assume that the population or sample is normally distributed. What is Probability Distribution
When sample size is large, even non-normal data leads to approximately normal distribution of sample means (by Central Limit Theorem).
(3) Central Limit Theorem (CLT)
CLT states:
When we take large samples from any population (not necessarily normal), the distribution of sample means tends to become approximately normal, with mean = μ and standard deviation = σ/√n.
This is why the normal distribution becomes the backbone of sampling theory and many advanced statistical methods. What is Probability Distribution
(4) Quality Control and Industrial Applications
In industries, normal distribution is used for:
Control charts
Monitoring production quality
Detecting whether a process is under control
Many quality characteristics (like dimensions, weights of products, etc.) are assumed to follow a normal distribution. What is Probability Distribution
(5) Finance and Economics
Used in modelling stock returns, asset prices, etc.
Helps in risk analysis, portfolio management, and forecasting.
Many financial models initially assumed returns to be normally distributed (though in reality they may be slightly different, but normal is used as an approximation). What is Probability Distribution
(6) Education and Psychology
Test scores (e.g., aptitude tests, IQ tests) are often near-normal.
Normal distribution helps in:
Setting cut-off marks
Grading on a curve
Comparing performance of students
Example:
If marks in an exam are normally distributed with mean 50 and σ = 10, then:
Students scoring above 70 are in the top few percent
Students below 30 are in the bottom few percent. What is Probability Distribution
(7) Probability Calculations with Z-Table
For a normally distributed variable, we often need to find:
P(X ≤ a), P(X ≥ b), P(a ≤ X ≤ b), etc.
We convert X to Z using: z = x – u/ (μ).
This is very common in exam questions and practical problems. What is Probability Distribution
5. Conclusion
A probability distribution describes how probabilities are assigned to different values of a random variable.
The normal distribution is the most important continuous probability distribution in statistics. What is Probability Distribution
It is bell-shaped, symmetrical, and fully defined by its mean and standard deviation.
Many real-life variables follow approximately normal distribution, and due to the Central Limit Theorem, it becomes the foundation of statistical inference, quality control, finance, education, and scientific research.
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STATISTICAL ANALYSIS FOR BUSINESS you must visit on the official website as Gndu.
What are the different types of slide layouts available in PowerPoint ? Explain with examples.
In PowerPoint, a slide layout means the ready-made arrangement of placeholders on a slide (for title, text, pictures, charts, etc.).
When you choose a layout, PowerPoint automatically sets where each type of content will appear. Types of slides in Power Point
Below are the main types of slide layouts (names may differ slightly in different versions), with clear explanations and examples.
Use: For the first slide of the presentation (cover slide).
Placeholders in this layout:
One big box for Title
One smaller box for Subtitle
Example: For a presentation “Uses of Computers in Education”:
Title: “Uses of Computers in Education”
Subtitle: “Presented by: Hira Lal, B.Com (Sem–II)” Types of slides in Power Point
This slide introduces the topic and the presenter.
2. Title and Content Layout
Use: For normal content slides after the title slide. It is the most commonly used layout.
Placeholders in this layout:
One box for Title at the top
One large Content box (in the middle) where you can insert:
Bulleted or numbered text
Pictures
Tables
Charts
SmartArt
Video, etc.
Example: Slide title: “Advantages of Email” Content (bulleted list in the content box):
Fast communication
Can send attachments
Low cost
Can be used worldwide
This layout is ideal for explaining a single point with supporting text or objects. Types of slides in Power Point
3. Section Header (or Title Section) Layout
Use: To separate different sections of a presentation, like chapter headings.
Placeholders in this layout:
One large Title placeholder
One Subtitle or text placeholder (sometimes smaller, below the title)
Example: In a presentation on “Computer Fundamentals” you may have:
Title: “Section II: Input Devices”
Subtitle: “Keyboard, Mouse, Scanner, Microphone” Types of slides in Power Point
This slide tells the audience that you are starting a new section.
4. Two Content Layout
Use: When you want to compare or show two things side by side.
Placeholders in this layout:
One Title box at the top
Two content placeholders next to each other (left and right)
In each content box, you can add:
Text
Picture
Table
Chart
SmartArt, etc. Types of slides in Power Point
Example: Title: “Hardware vs Software”
Left content box (Hardware):
Text:
Physical parts of computer
Touch and see
Examples: CPU, keyboard, mouse
Right content box (Software):
Text:
Set of instructions
Cannot be touched
Examples: MS Word, Windows, Tally
This layout makes comparison clear and easy to understand. Types of slides in Power Point
5. Comparison Layout
Use: Very similar to Two Content, but also gives small headings for both sides.
Placeholders in this layout:
One Title box at the top
On the left side:
A small heading box
A content box
On the right side:
A small heading box
A content box
Example: Title: “Printer vs Plotter”
Left side:
Heading: “Printer”
Content:
Prints text and images on paper
Generally used for normal documents
Types: Inkjet, Laser Types of slides in Power Point
Right side:
Heading: “Plotter”
Content:
Used for large drawings
Used by engineers and architects
Very high-quality line drawings
This layout is very good when you want to compare two items with headings.
6. Title Only Layout
Use: When you only need a title, and you will manually insert other objects anywhere on the slide.
Placeholders in this layout:
One Title box at the top
No fixed content box. The rest of the slide is empty.
You can then insert:
Pictures
Text boxes
Charts
Shapes etc., and arrange them freely.
Example: Title: “Growth of Sales (2019–2024)” Below the title, you manually insert a chart and maybe a text box with comments. Types of slides in Power Point
This layout is useful when you want full design freedom.
7. Blank Layout
Use: For a completely empty slide with no placeholders at all.
Placeholders in this layout:
None (no title, no content)
You can add anything:
Text boxes
Pictures
Shapes
Charts
SmartArt and place them exactly where you want.
Example: You want to create a full-slide image:
Insert a high-quality picture of a “Computer Lab”
Resize it to cover the entire slide
Optionally, add a small text box in a corner: “Modern Computer Lab”
This layout is used mainly for creative design or image-only slides. Types of slides in Power Point
8. Content with Caption Layout
Use: When you want to show a picture or object with an explanatory text beside or below it.
Placeholders in this layout:
One Title box
One main Content box (often for a picture, chart, or diagram)
One Caption text box (for explanation)
Example: Title: “Block Diagram of Computer System” Types of slides in Power Point
Main content:
Insert a diagram that shows Input → Process → Output → Storage
Caption:
“This diagram shows the basic working of a computer where input data is processed by CPU to generate output, and results may be stored for future use.”
This layout is perfect for figures, diagrams, and photos with explanation.
9. Picture with Caption Layout
Use: To show one main picture with a caption and sometimes a title.
Placeholders in this layout:
A large picture placeholder
A Caption text placeholder (usually below the picture)
Sometimes a separate Title box at the top (depends on the theme)
Example: Title: “GNDU Campus”
Picture: A photo of GNDU University campus.
Caption: “Guru Nanak Dev University, Amritsar – Established in 1969, known for excellence in higher education.” Types of slides in Power Point
Useful when you want to highlight a single important image with a short explanation.
10. Other Layouts (depending on version/theme)
Some PowerPoint templates or versions also show layouts like:
Title and Vertical Text – Title on top and vertical text on the side.
Vertical Title and Text – Vertical title and normal text.
Title and Chart, Title and Table – Where the content box is pre-set for charts or tables.
These are just special cases of content layouts where PowerPoint assumes the main content type. Types of slides in Power Point
Summary
Slide layout decides the arrangement of title, text, and other objects (picture, chart, table, etc.) on a slide.
Common layouts available in PowerPoint are:
Title Slide – for first/intro slide with title and subtitle.
Title and Content – for main content slides with text, pictures, charts, etc.
Section Header – to start a new section in the presentation.
Two Content – to show two pieces of content side by side.
Comparison – to compare two items with headings on both sides.
Title Only – only title; rest of slide can be designed freely.
Blank – no placeholders; completely empty slide.
Content with Caption – object with explanatory text (caption).
Picture with Caption – big picture with caption and sometimes title.
Each layout helps to present information clearly and attractively by giving a suitable structure to the slide. Types of slides in Power Point
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